Twine, 22, was the League One player of the season last term, after scoring 20 goals and claiming 13 assists in his first season with the Dons, after signing from Swindon Town at the end of his dal at the County Ground.
The Clarets have reportedly made a £4million offer for the forward, who can play as a number 10, on the left or as a striker, while Hull City are a,lso thought to have offered £3m.
Manning, speaking to BBC Three Counties Radio, said that those bids are not enough as things stand: "Naturally, you're going to get that interest, obviously, given how well he did.
"He was the League One Player of the Year but, as it stands, we have not had a bid that meets our valuation of him.
"There's obviously interest in him, but we're in a good, strong position where we can be quite strong in the valuation we hold and expect for him.
"It's like I said a little while ago - if somebody's journey goes quicker than the team's and it's a fair deal for the club and a fair deal for the player, then it's something that you look at.
"But, as it stands, we know there's interest, but there's not been a bid that meets our valuation. There have been a couple of bids, but they're not where they need to be yet."
Manning has been impressed with Twine’s professionalism amid the speculation: "It sums him up as a person. He's in here working. He did the testing like everybody and that comes down to the culture here.
"We'll treat you as a person first and have open communication.
"We'll treat you properly and we expect that back and Twiney is a terrific character, so you wouldn't expect anything different from him."
Swindon-born, Twine was with Royal Wootton Bassett Town as a youth before joining the academy at Southampton, moving to hometown club Swindon Town in 2013, and signing professional terms in 2017, making his first team debut on the final day of the 2016–17 campaign as a substitute at Charlton Athletic.