The Croatia international has been linked with a move to Old Trafford for a number of weeks but no agreement has yet been reached over a deal.
United boss Jose Mourinho admitted last week that he had "no idea" if Perisic would join the club and the winger has been involved in Inter's pre-season plans, starting the 1-1 friendly draw with Schalke on Friday.
Spalletti insists that he would like to keep the 28-year-old but admits that he could be allowed to leave if a sizeable offer were made that would allow for further investment in the squad.
"He is a fantastic player and if his future is totally up to me, I will definitely keep him," Spalletti told a media conference.
"However, if an offer comes and the club are satisfied with the money, which will be used to invest in and strengthen the team, he could leave."
United had initially hoped to use Inter’s desperation to meet Financial Fair Play commitments in order to prise away Perisic for a fee of around £26.4m, but the Serie A club were able to raise the funds from elsewhere.
Perisic remains keen to leave San Siro for the Premier League and ordered his agent to do everything necessary to force through a deal with United.
The Premier League club have continued to haggle over a fee with Inter, who are understood to be ready to accept an offer in the region of £40 million .