Duff has been on Cheltenham's books since leaving school in 1999
Cheltenham Town have given defender Shane Duff until the end of next week to accept a new deal.
Duff, 27, whose contract expires at the end of June has been considering the offer made at the start of May.
"He has the right to shop around to see if any other clubs will take him and maybe pay him more money," Allen told BBC Radio Gloucestershire.
"Shane Duff's shown that he's a leader and he would be a good person to help bring our younger players on."
Allen also refused to put a figure on the number of signings he wants to make this summer.
The Robins currently have only 13 professionals under contract for next season and two of those - John Finnigan and Josh Low - are on the transfer list.
Allen had previously stated ideally he would want 19 in the squad but he is now reluctant to reveal a figure.
"If I don't get to it then the supporters might be disappointed so I'd rather keep that sort of target to myself," added Allen.
"There is a strict budget that we have to work to and we're not going to get into the position that we were in at the end of last season. I never ever want to go through that again."
"We've got some very good youth players and they may have to be used more often."
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