Sullivan, a life-long Irons fan, has, along with business partner David Gold, a former youth team player at Upton Park, acquired 50% of the Barclays Premier League outfit in a deal which values the club at £105million and gives the duo operational and commercial control.
McCarthy, 32, almost joined West Ham from Porto five years ago, and has been linked with a switch to east London.
Upton-bound: Benni McCarthy in action for Blackburn, where he has fallen down the pecking order
Hammers co-owner David Gold said: 'He would be a good acquisition,if that could be achieved. It's possible, but all strikers that areavailable as we speak are possible.'
Gold added on Sky Sports News: 'It is a question of 'can we do business?''
The new owners met on Wednesday with Zola and assistant manager Steve Clarke to discuss the way forwards.
'I was hugely impressed with Gianfranco and Steve,' Sullivan said in the London Evening Standard. 'It is so great to meet a man who wants to work with us and make the team better.
'He has a 'can-do' attitude, but with a pragmatic approach. Gianfranco is a really nice guy. I believe he can be a great manager.
'We agreed we need at least one striker by the Portsmouth match and the second by the end of the window.'
Sullivan will look to free up as much funds as possible, believed to be around £8m, after pledging no players needed to be sold.
There had been speculation the likes of centre-back Matthew Upson, goalkeeper Robert Green and striker Carlton Cole, as well as midfielder Scott Parker, would have to be sold off to help balance the books.
Sullivan revealed West Ham had been under pressure to bring in some £8m during the current window, and more by the summer, a scenario which now was no longer on the horizon due to their takeover.
'Matthew is the captain and his return to the team in recent weeks has coincided with improved performances,' said Sullivan, who is also likely to be on the lookout for some defensive cover this month.
'We all agreed that Scott, despite a lot of interest, is going nowhere. He is a wonderful player, the heartbeat of the team. Despite the difficult times, he has always been up for the challenge, always fighting for the badge.'
Sullivan intends to deal with transfers himself, leaving the future of technical director Gianluca Nani unclear.
The arrival of Karren Brady as vice-chairman completes the Birmingham connection at Upton Park, but her salary will be met by Sullivan and Gold rather than the club.
Indeed the duo will themselves not take a wage as the new regime look to cut costs and reduce the enormous debt levels, which are owed to both banks and other clubs, including settlements to Sheffield United over the Carlos Tevez affair and former manager Alan Curbishley.
New era: David Sullivan (left) and David Gold pose for media
'We are fully behind the manager, but I do not want to go into all staff,' Sullivan said. 'There may be some changes at some level, we are going to look at all sorts of things. We do not rush into decisions.'
Sullivan added: 'There has to be some savings here. This is a club haemorrhaging money. There may have to be economies, and there is no point saying otherwise.
To put things in perspective, I will be earning nothing, David will be earning nothing. We are personally paying Karren's wages for the next 12 months so she is not a burden to the club at all.
'We are not coming here with baggage which will cost the club money, we are all going to make a contribution at zero cost to the club.'
Sullivan openly admits buying West Ham made no business sense, but believes now with fans in the boardroom, the future can be bright.
The new owners have an option to buy the remaining 50% from Icelandic bank Straumur in the next four years, but hope other wealthy supporters, including Lotus F1 supremo Tony Fernandes, whose rival takeover bid was unsuccessful, can provide more investment.
'Unfortunately we are inheriting these liabilities, and are going to have to work through them,' Sullivan said. 'Every stone you turn is a negative to the cash-flow of the club.
'We are taking over an incredibly bad situation. However, we will sort it out abecause we are good at it.'
£100m Hammer horror: Sullivan and Gold vow to dig West Ham out of messDavid Sullivan completes West Ham takeover deal: Full statementALL THE WEST HAM FC