The Croatian international has been rumoured to join Gunners during the transfer window, with speculation mounting since he handed in a transfer request on Saturday.
Perisic was subsequently left out of the Inter squad a day later as the Nerazzurri went down 1-0 against Torino.
Inter director Piero Ausilio revealed the Serie A side are yet to be satisfied by any offer for the 29-year-old attacker, with reports Arsenal had a loan bid with an option to buy for €40 million rejected.
It's understood they are open to let Perisic leave but only on a permanent deal or a loan with an obligation to buy.
"Perisic wants to go abroad, but there are no suitable offers," Ausilio said.
"If he does remain, I expect the same professionalism from him as always. We intend to get him back on track and it shouldn't be a problem. I don't think it'll take very long.
"I can say the Inter transfer market is closed. We had some fitness issues with Sime Vrsaljko and did well to immediately cover the gap with Cedric Soares [from Southampton].
"Inter have had a difficult path over the last few years, having changed ownership three times, but we now have a solid and ambitious owner who with time and patience can achieve great things."
The Milan club have failed to score in either of their Serie A matches since the winter break finished, and currently sit third in the Serie A - 19 points behind leaders Juventus.