Calciomercato understand an offer of £31million would be enough to force the Italian's hand.
Since the World Cup, the Croatia international has failed to hit the heights of previous seasons, scoring just twice in 16 appearances this term.
United pursued the 29-year-old for much of last summer but failed to lure him to Old Trafford.
Executive vice-chairman Ed Woodward is regarded as being central to the failure to secure the wideman.
Inter set their valuation of Perisic at £48million in the summer.
But Woodward was only prepared to go as high as £45million, and steadfastly refused to budge.
The saga unfolded 12 months after an offer of £40million was said to have been accepted, but the move never materialised.
It also followed the arrival of Alexis Sanchez, who joined from Arsenal in January on a contract worth £500,000-a-week.
Mourinho ended last summer with just three new faces in the form of Fred, Lee Grant and Diogo Dalot.
The succession of failures in the market has contributed to them falling 12 points behind Premier League leaders Manchester City after a dozen games, leaving their title ambitions in tatters.
Perisic is said to be close to Inter boss Luciano Spalletti and he revealed last year the manager played a key role in keeping him in Serie A.
He explained: "He said that all the players are important, even those who played less so far have done well.
"The coach was very important to convince me to stay. I waited a long time for this moment."
But it remains to be seen whether Spalletti's powers of persuasion will be enough this time around.
Inter have reportedly been warned by Uefa that they risk breaching Financial Fair Play regulations if they do not stump up £44m before the end of next June – potentially raising the possibility of a fire sale.
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