Real Madrid manager Rafael Benitez says both club president Florentino Perez and Manchester United target Sergio Ramos are optimistic of their stand-off coming to a positive conclusion.
The defender and Real have been locked in a contract impasse after negotiations to renew his current contract at the Santiago Bernabeu stalled in June.
According to BBC Sport and Spanish newspaper El Pais, United have made two bids for the Spain international, the latter of which was worth €60m (£42.6m, $66.1m) but so far Real have refused to contemplate selling the man who will replace Iker Casillas as club captain.
Marca has claimed Ramos and Perez have maintained a frosty relationship ever since initial contract talks broke down, with Benitez forced to act as an mediator between the two.
But speaking after Real's 3-0 win over Inter Milan on their pre-season tour of the United States, Benitez appeared confident of a resolution being met, also confirming reports of a meeting between both parties on Sunday 26 July.
"I spoke to the president on Sunday at lunch and he told me that he hoped to speak with Ramos," Benitez told a press conference, AS report. "I've asked both and they seem to be optimistic. We will see.
The Guardian reports that the meeting between Ramos and Perez, which also included Real's chief executive Angel Sanchez and Ramos's brother and agent, Rene, saw the club maintain their position that the defender will not be sold under any circumstances.
United have been similarly resolute in their handling of goalkeeper David de Gea, who remains linked with a move to the Santiago Bernabeu and have insisted the Spaniard will not be sold unless Ramos is allowed to join them.
United manager Louis van Gaal has been coy on the club's chances of bringing Ramos to Manchester. When quizzed over United's pursuit of the defender at a press conference earlier in July, he told reporters: "Maybe Mr Ramos is in the process."