Torreira only joined Arsenal last summer, arriving as the most expensive of Unai Emery’s five new additions.
The Uruguayan has impressed for the Gunners during his first 12 months at the club.
However, recent reports suggested he was unhappy in London and was seeking a return to Italy.
AC Milan are the club reportedly interested in poaching Torreira this summer.
But the former Sampdoria man has spoken out while on international duty at the Copa America – and he has reassured Arsenal fans he is happy to stay.
“Nobody from AC Milan has got in touch with me, today I’m in the Premier and happy to be part of the Arsenal,” he said ahead of Uruguay’s game against Peru on Saturday.
“It cost me the adaptation, it’s not easy, but I only think about that team.
“I’m happy to be there.”
Should Torreira leave Arsenal this summer, Emery will keen to replace the player in the middle of the park.
However, according to BBC reporter David Ornstein, the north London club are more than confident that the 23-year-old will remain beyond the summer.
“Another of their key assets is Uruguay midfielder Lucas Torreira, who arrived at Emirates Stadium from Sampdoria last summer and has been linked with a return to Italy,” he wrote.
“But while Arsenal accept every player has a price, they have no intention of letting the 23-year-old go and do not believe he is unhappy, contrary to some reports.
“Torreira has been most heavily linked with AC Milan and although they do admire him, he is not a focus of their attention – the Rossoneri know the asking price would be prohibitive and have other targets.”
Arsenal continue to be linked with a host of players despite the fact the club have limited funds to spend before the August 8 deadline.
Emery is reportedly set to receive £45m to spend on players – plus whatever money is brought in from stars leaving.
Arsenal have been linked with Yannick Carrasco, Ryan Fraser and Ivan Perisic in recent weeks.