There had been doubts that Reyes, whose two goals on the final day of the Primera Liga season helped Real beat Real Mallorca 3-1 and become Spanish champions for the first time since 2003, would remain at the Bernabeu when his season-long loan from the Gunners ran out.
However, Real sports director Pedja Mijatovic has hinted that a possible deal may be in the pipeline for the Spanish international.
"(Reyes) helped us win the league. He's an excellent player and there's a chance he'll stay with us," he said.