The ex-Newcastle Falcons lock's existing deal expires at the end of the season and the Tigers expect plenty of interest in his signature.
Leicester want to retain the 29-year-old, but are concerned about retaining the bulk of their key personnel and staying inside the salary cap.
"We would like to keep Geoff Parling and have made him a good offer," chief executive Simon Cohen told the Leicester Mercury.
"Undoubtedly, he will be able to get more elsewhere. The difficulty for us is getting the amount of people that we need in the squad within the salary cap.
"Geoff will have to work out whether it is worth taking slightly less money in return for the benefits of being in our system."
Parling has been away from the Aviva Premiership club of late after representing England in their Autumn Series Internationals, but hopes his contract will be "sorted out" soon.
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