Everton have told German side Hamburg they will have to double their offer for Danish midfielder Thomas Gravesen.
Hamburg made a bid of under £2m last week and coach Klaus Toppmoller admits he still wants to buy the 28-year-old.
But BBC Sport understands the Goodison Park club will want at least £3.5m before they consider selling Gravesen.
With the cash injection from chairman Bill Kenwright, Everton may decide to keep Gravesen until next summer, though he would then be available for nothing.
Everton offered the Dane a new contract in the summer but he has so far refused to sign, saying he would like to be playing for a club that is in European compeition.
Gravesen signed for Everton for £2.5m from Hamburg in 2000.