Shaqiri has scored 15 goals in 92 appearances for Stoke since joining the club back in 2015 but the 26-year-old winger will leave the Potters after they were relegated from the Premier League.
Reports suggest Liverpool have held talks with Shaqiri over a £12million move to Anfield but its understood the Reds will have competition from bitter rivals United this summer.
According to The Sun, Mourinho was keeping an eye on Shaqiris displays at the World Cup before Switzerland were eliminated at the hands of Sweden in their last-16 clash.
Its claimed Mourinho has even told close friends that hes keen on the former Bayern Munich man.
Shaqiri confirmed earlier this week that he will leave Stoke this summer, but stressed that he plans on remaining in England.
I want to stay in the Premier League and you will find out my new club soon, the Switzerland international said.
Amid speculation linking him with Liverpool, Shaqiri admitted that the chance to play at Anfield was appealing.
Asked what he thought of Liverpools iconic stadium last month, Shaqiri chuckled before replying: The Anfield stadium is great certainly.
But why are you talking about Liverpool?
Shaqiri is tied into a deal at the bet365 Stadium until the summer of 2020.