The 24-year-old was on a list of forward options Mourinho gave to executive vice-chairman Ed Woodward before the end of last season.
It had been thought Lukaku, who scored 25 Premier League goals last season, would rejoin his former club Chelsea.
However, United now feel it is possible to get the Belgium international.
The club have been in negotiations to sign Alvaro Morata from Real Madrid, but have so far been unable to reach an agreement.
United are already in contact with Everton over a deal for former England captain Wayne Rooney, who is likely to leave Old Trafford and return to Goodison Park.
That could make negotiations relatively smooth, even if the fee being spoken of would challenge the world record £89m transfer that took Paul Pogba to Old Trafford from United last summer.
Lukaku was sold to Everton for £28m by Mourinho during the Portuguese manager’s second spell in charge of Chelsea in 2014.
He is a client of agent Mino Raiola, who also looks after Pogba, Zlatan Ibrahimovic and Henrikh Mkhitaryan – three players all signed by United last summer.
The Belgian turned down the most lucrative contract offer in Everton’s history in March and later said: “I don’t want to stay at the same level. I want to improve and I know where I want to do that.”
A Freelance Journalist, Entrepreneur and Philanthropist. Editor-in-Chief of www.233times.com. A contributory writer for Ghanaian Chronicle Newspaper. An alumnus of Adisadel College where he read General Arts. He holds first degree in Bachelor of Arts from the University of Ghana; Political Science (major) and History (minor). He has also pursued MSc Corporate Social Responsibility (CSR) and Energy with Public Relations (PR) at the Robert Gordon University in the United Kingdom. His mentors are Rupert Murdoch, Warren Buffet, Sam Jonah, Kwaku Sakyi Addo and Piers Morganview all posts by: Nana Kwesi Coomson
233times.com is a Ghanaian media house which serves as a major source of exclusive interviews ,music and video downloads, news and more.
233times.com reports on major events,news covering entertainment, politics, sports, etc from within Ghana, Africa and beyond.
We have a platform for the amateur artistes to portray their staggering talents ...more...
To advertise with us or make enquiries, please visit 233times.com/advertise or call +233249455142 (Selorm), +233248185848 (Nana Kwesi)