Everton, annoyed at Fenerbahce's penny-pinching, want the 31-year-old back at Finch Farm in early July if no agreement is reached by then.
The Nigeria captain is in his second one-year loan spell with the Turkish club, with the initial arrangement being for Fenerbahce to sign him on for a £5-million transfer fee at the end of the loan.
But Fener are now baulking at the agreed price and have instead offered Everton £1-million.
Yobo has been a key fixture for Fenerbahce, having played all but two games in his two seasons there and quickly becoming a fan favourite.
This season, he was an integral part of the side that narrowly missed out on the league title, but won the Turkish Cup and qualified for the Champions League.
Sources close to the Turkish side say that while Fenerbahce have been impressed by Yobo's performances in his time with them, their valuation is based on the player's age, meaning there is virtually no resale value.
Fenerbahce are also aware that Yobo is on a lucrative contract at Everton, one that still has two years to run and which the finances at Goodison Park can barely afford to continue servicing.
Neither the Everton nor the player are keen on continuing that relationship, and Fenerbahce are looking to cash in on that.
Expectations from both sides is that an agreement can be thrashed out at around £2-million.