Idrissa Gueye remains intent on pursuing a move to Paris Saint-Germain.
Everton rejected a £21.5 million approach from the French champions during the January window, with Marco Silva insisting that the midfielder was not for sale.
But the Telegraph claim that Gueye, who was voted the club’s Players’ Player of the Year last season, is hopeful of Les Parisiens returning with an improved offer.
Fabian Delph’s arrival from Manchester City could pave the way for the Blues to countenance a renewed approach from PSG for the Senegal international.
Gueye, 29, is currently away on international duty as his homeland prepare to take on Algeria in the Africa Cup of Nations final on Friday.
Silva has admitted that he is keen on making further additions to his ranks at Goodison Park before the English transfer window closes on August 8.
Delph’s £8.5m move became Everton’s third signing of the summer, following in the footsteps of Andre Gomes and Jonas Lossl’s respective switches.
“I would prefer that the players are here already but in the market, it’s not easy,” Silva told evertontv.
“The deals you want to do are difficult deals also because we want just players who can strengthen our squad, to improve our squad.
“Let’s see what we can do.”