QPR loanee Tom Carroll wants to "make it at Tottenham" but is prepared to consider all of his options at the end of the season.
Ilkay Gundogan has commited his future to Borussia Dortmund by signing a new contract.
On Monday the Toffees announced they had agreed an £8.6million fee with the Dutch club and the 23-year-old travelled to Merseyside to discuss personal terms and undergo the usual routine health checks.
However, Press Association Sport understands during those assessments medical staff identified an issue which raised enough concerns for Everton to go back to Twente in an attempt to renegotiate the deal.
Instead of the full fee up front the Premier League side wanted to pay a smaller amount with the remainder dependent on appearances and other factors.
Twente have rejected the new terms and although negotiations are continuing the move is in the balance.
If it is not wrapped up in the next 24 hours Everton will not allow it to drag on into the final day of the transfer window.