The 23-year-old, who can also play at fly-half, is out of contract in the summer and he has been linked with a move to Gloucester.
And director of rugby Richard Cockerill has expressed his disappointment that Twelvetrees, recently selected in the England Saxons squad, will not stay with the east midlands club to battle Anthony Allen and Manu Tuilagi for a midfield spot.
Cockerill told the Leicester Mercury: "Billy has played for us in every game he has been available apart from two this season.
"We have put three years of development into Billy and he was coming on nicely in our environment.
"If he does not want to stay and fight for his spot, that is disappointing.
"Scrum-half Micky Young joined us last summer and knew he would have to fight for his spot with Ben Youngs.
"Ed Slater would cut off his arms to play for us on a regular basis, but he battles for a spot with Louis Deacon, Geoff Parling and George Skivington."
Cockerill added: "That is the way it has been for more than 100 years and that is the way it is going to stay.
"There are world-class players holding tackle bags in training every week."
If Twelvetrees, who has started in 12 of his 13 appearances to date this term, should depart in the summer Leicester are likely to need to recruit cover at outside-half and centre, with Jeremy Staunton also tipped to move on.
"We are in the process of bringing new players in and there is a lot of quality out there that we are looking at," said Cockerill.
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