The Finland striker has reportedly been attracting interest from other clubs managers, most notably Villa boss David O'Leary.
“I like him yes, but I’ll say no more. He’s young and I think someone like him would improve us immensely," O'Leary told his clubs official website on Friday.
However, Sullivan has scoffed at this statement claiming Blues have an agreement with Chelsea to extend the Finns stay at St. Andrew's.
"This is a very silly statement to make. If there is one club Forssell couldn't play for then it is Villa, Sullivan told the Birmingham Sunday Mercury.
"The grief he would get in the city is unbelievable. I don't think David O'Leary can understand how things work in the city. If we were looking to off-load a player we would let him go to any other club apart from Villa unless we were in dire financial straits.
"We have an understanding with Chelsea, and they are a very honourable club, that Forssell will be with us for the rest of the season. I am sure we can then open negotiations on a permanent transfer.
"O'Leary is wasting his time. I can't understand why he is doing this, because it will cause unpleasantness and unrest."