Sheffield United boss Bryan Robson is expected to sell Phil Jagielka to Everton this week.
United had wanted to keep hold of the defender in case they stay in the Premiership but, as that looks unlikely, Everton need to raise their bid to trigger a £4 million get-out clause in Jagielka's contract.
So far, Everton have offered £2.5m plus Gary Naysmith, but Sheffield United value Naysmith at only £500,000.