Off contract in June, the defender is attracting interest from Fenerbahce.
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However, Atletico haven't written off keeping Reinildo and are ready to draw up a new contract offer for his consideration.
For his part, the 30 year-old is yet to make a definitive decision about next season, says Mundo Deportivo.
The left-back, who can act as a centre-back, is also said to be on the radar of Barcelona.
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