The club have received no offers for the Belgian striker and intend to keep him at Villa Park for the foreseeable future.
Benteke, 24, has been excellent form since Sherwood arrived at Villa, bagging 12 goals in the past 12 games to help the club secure both Premier League survival and a place in the cup final.
However, his impressive performances have caused speculation about his future to go into overdrive in recent weeks, with a host of top clubs now being linked with a summer move for the Belgian striker.
However, speaking ahead of the Gunners clash, Sherwood seemed to tell the likes of Liverpool to forget about pursing his star man, declaring: "We have no offers for Christian and it's not worth talking about until we do.
"We are happy with him here and we hope he is here for many years to come."
Of course, Sherwood might not have much choice but to sell Benteke if the front man does demand a move this summer but, for the moment, he has given no indication that he intends to leave.
Moreover, winning the FA Cup this weekend and place in the Europa League as a result might just prove the ticket to convincing the former Genk forward to stick around, and the Villa boss is optimistic about his side’s chances of causing an upset.
"I thoroughly believe we will get a performance like the one we put in against Liverpool [in the semi-final]. You have to believe that,” added Sherwood. "Hopefully we can nullify Arsenal's threats and take the game to them. That's what we intend to do.
"Arsenal are the favourites. They've been there and done it before. They are the holders of the trophy. It will be very difficult for us but we're not going there to make the numbers up. We aim to give them a good game.
"I know what the boys are capable of and they have proved that in this FA Cup run. On the big occasions they have produced the goods. They need to do it one more time.”