The Sun is reporting that Manchester United are optimistic that a deal can be struck with the Serie A giants to secure the transfer of the Croatia international.
However, the story goes on to reveal that Real Madrid striker Alvaro Morata remains the number one target for the 20-time English champions this summer.
The 28-year-old Perisic has emerged as a target for the Red Devils in the 2017 summer transfer window despite some concerns about the size of his transfer fee.
Reports earlier this month suggested that Inter valued the former Wolfsburg winger at around £48m following the appointment of Luciano Spalletti as their new manager.
However, Manchester United are said to be unwilling to pay more than £35m for the versatile winger in the summer transfer window.
Mourinho led Manchester United to a sixth-place finish in his first season in charge at Old Trafford.
But the Portuguese coach did win the EFL Cup and the Europa League.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news