The Gunners had tabled an improved bid for the Portugal international on Saturday as Arsene Wenger looked to recruit a midfielder with physical presence.
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But the 22-year-old - who has also been linked with Manchester United and Chelsea this summer - has now gone public to reiterate his commitment to Sporting for the foreseeable future.
"I am under contract with Sporting and I'm a Sporting player," he told A Bola. "There is no way I can say I am going to leave. I am fine at Sporting."
Arsene Wenger will spend the final few hours of the transfer window refereeing a charity 'Match For Peace' in Rome and club sources do not expect a busy day in terms of arrivals.