But they could also potentially play as many as 23 extra matches should they go all the way in the Europa League after qualifying via the FIFA Fair Play route despite finishing the Premier League season in 12th place.
Both Sullivan and fellow co-owner David Gold had pledged to invest 'significantly' this summer and have already signed goalkeeper Darren Randolph from Birmingham and Spanish U21 international Pedro Obiang from Sampdoria.
There is more good news for Hammers fans on the way, though, as Sullivan - who takes a leading role in West Ham's transfer business - has given a frank assessment of what is needed to beef up the East Londoners' squad.
"Definitely four or five signings you know, and one or two very, very exciting players that we really like and the new manager really likes which is very important," Sullivan told West Ham's official website.
"Some will be very highly paid Bosmans (free transfers), others will be big transfer fees, slightly lower wages, but we know we need to strengthen that squad."
Just who those exciting players are is anyone's guess as the Hammers have been linked with a host of players including Chelsea striker Loic Remy, Queens Park Rangers' Charlie Austin, Paris St Germain's Yohan Cabaye and Marseille's Dmitri Payet.
West Ham's season will start before any other Premier League team with their first two-legged Europa League qualifier on July 2.
That means former Besiktas boss Bilic, who has experience of juggling the demands associated with playing domestic and European football, has just two weeks to get his squad ready for that early start.
If Sullivan is true to his word, though, it would be no surprise to see the Hammers being active in the transfer market right up until the window slams shut on September 1.