Arsenal have reportedly been knocked back by La Liga champions Atletico Madrid with a £9m approach for Juanfran.
The Gunners are said to be keen on identifying a swift replacement for Bacary Sagna, who recently confirmed that he will leave the club this summer.
However, according to The Mirror, the 29-year-old Spaniard wants to remain in the Spanish capital, forcing manager Arsene Wenger to extend his search for a new right-back.
Wenger has also been linked with a move for Schalke 04 defender Atsuto Uchida.
Juanfran's contract at the Vicente Calderon expires in 2017.