Stoke fancy Crewe ace
Brammer's contract with The Railwaymen expires in the summer and he is still wanted by Crewe boss Dario Gradi.
But Gradi is unable to offer the 29-year-old the same terms and that has prompted Brammer to mull over his options with Stoke and Coventry among his suitors.
The influential midfielder missed a chunk of the season through injury but he has been a key figure at Gresty Road since joining in a £500,000 deal from Port Vale three years ago.
However, his agent has warned Crewe that Brammer is by no means certain to stay at the club as he is likely to have better offers elsewhere.
"I would think Dave would want to stay in the First Division," Mickey Walsh told the Sentinel.
"I have spoken to him and there has not really been a formal offer from Crewe.
"But I had a conversation with Dario Gradi before the season finished and he wants to keep Dave.
"He realises he can't pay him the contract he is on now and the discussion was left there.
"Since then there has been interest from Stoke and Coventry, although nothing concrete as yet.
"Dave is not saying no to Crewe but he feels he is in a position where he can see what is on offer at other clubs."