For some months, Modric has been leaning towards making this his last season in Madrid. The midfielder wants to wind down his career at a club where there are less demands.
The Croatia international is also seeking one final major payday, but Real president Florentino Perez has no plans to offer him a new contract.
Diario Gol says a return to England and former club Tottenham is favoured by Modric, though he also has fielded interest from AC Milan this season.
Cristiano Ronaldo, meanwhile, is working on Modric not to leave him this summer. The pair are good friends and Ronaldo fears for Real's midfield should their prime playmaker choose to depart.