Here, in part two, Mr Sullivan talks about how the squad could improve further, the final season at the Boleyn Ground and the upcoming move to the New Stadium. Remember, you can watch the full video interviews now by clicking the video player below or by visiting the Club's official YouTube channel.
West Ham United Joint-Chairman David Sullivan believes the ambition of a top-six finish is not beyond the realms of possibility, given the quality of West Ham United's start to the season.
While Mr Sullivan admits that the financial power of the leading Barclays Premier League sides is hard to compete with, the team's impressive performances thus far means the Club can aim high. He believes the upcoming run of fixtures presents an opportunity to return more points and possibly climb higher than their current seventh place in the Barclays Premier League table.
"I've said right at the start we can finish sixth and I think it's possible," Mr Sullivan said. "We could be on 18 points now. It's not a dream - we just needed a bit of luck in three games where we didn't get what we deserved. I don't think we've had a single game this season where we got more than we deserved out of a game.
"We've had three games where it wouldn't have taken a lot get more than we got. If we got points out of them, you're moving towards sixth place.
"I also realise things can go wrong but I think there are grounds for optimism. It's not rhetoric based on nothing, it's based on what we've achieved so far and the fixtures we've got coming up. If we play them like cup finals and play the West Ham way and score some goals, we could be in the top six.
"Whether we will is a bit of a tall order but it's not impossible. You've got to aim high and see where you finish."
While yesterday's interview focused on the new arrivals at the Boleyn Ground, the familiar faces of last season have also more than played their part this term. Stewart Downing, in particular, has won plaudits for his performances at the tip of Sam Allardyce's new diamond formation and the Joint-Chairman is delighted to see him flourishing in his new role.
"Stewart's like a different player and you'd have to thank Sam for changing the formation, which seems to suit him a lot better than just being a winger.
"All of his life he has been a winger, now he's in the diamond he's a much better player. His passing is fantastic and he'll score a few goals. On the wing he looked alright but he didn't look the special player we thought we'd signed, but he now looks like that special player."
The summer transfer window closed just six weeks ago, so for most it may seem a little premature to start planning for the next two windows; in January and next summer. But such is Mr Sullivan's meticulous eye for detail and planning that that is exactly what he is doing.
"We cannot go above the wage limit under the Financial Fair Play rules, so even if we want to sign players in January, we cannot sign someone unless someone leaves as those are the rules.
"There might be a deal that is too good to refuse that we can do if we've done a new commercial deal. There is an exception to every rule but we're not looking to sign five loan players that cost us £5-6 million like last season.
"We had to do that last season as we were such a small squad under such pressure - we had to get some cover in and it kept us up.
"We will always invest where we can and we'll look to improve again next summer but I don't want to give any figures yet. Just to reiterate, though, if we wanted to put money in we can't because you're restrained by your wages budget unless you have new commercial income."
January 2015 will mark five years since Mr Sullivan and his long-term business partner and friend David Gold took a controlling stake in West Ham United and in that time, the Club has seen impressive progress on the field, with two comfortable Premier League finishes in the last two years, substantial third-party debt reduction off it and a move to a stunning new home secured. Mr Sullivan feels there is still more work to be done, though, but is optimistic about the direction the Club is heading in.
"I wouldn't say I am happy with where we are yet, no. We never anticipated getting relegated, that put us back a year or two. It really hurt us financially and from a squad point of view as we had to let players go.
"If we finish in the top six this year that would be terrific, but up to now we haven't done enough.
"I think we are starting to get it right. We've signed young and attacking players and that's a change of philosophy. Our hope is that the Olympic Stadium can help fast-track our progress. It will give us a bit more to buy players.
"Anything is possible and you have to dream and I just don't subscribe to the fact that we've had a successful season if we finished 17th. That's not good enough for West Ham fans.
"I would love to be back in Europe, even with extra games. It would bring some of the glorious old days back to supporters. I think we may be making some progress towards that.
"I'm optimistic, the supporters are optimistic, the way the team is playing is fantastic and with a small bit of luck, we can have a fantastic season."