The latter never really made the grade at Stamford Bridge, being sold to Everton by Mourinho during his second stint at the club, only for the same manager to spend £90m to bring him to Old Trafford during the summer.
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After a blistering start to life at the club, Lukaku has failed to score in his last six appearances for the Red Devils, while questions have been asked about his record against the big clubs.
Here, Sports Mole looks at how he has fared against Chelsea since leaving the club on a permanent basis in 2014.
Having been ineligible to play against his parent club during loan spells at West Bromwich Albion and Everton, Lukaku finally got his first chance to prove himself against Chelsea after signing for the Toffees on a permanent deal in 2014-15.
Things did not start off too well for the Belgian, though, as he suffered defeats home and away to the Blues that season and failed to get on the scoresheet despite the two sides sharing 10 goals over the two meetings - including a 6-3 Chelsea win at Goodison Park.
Chelsea went on to win the title that season, but their subsequent defence was diabolical and Everton took full advantage with a 3-1 win at Goodison Park in September 2015, although Lukaku was not amongst the scorers as Steven Naismith helped himself to a hat-trick.
There were six more goals in the return fixture at Stamford Bridge, but once again Lukaku drew a blank despite playing the full 90 minutes as Chelsea rescued a dramatic 3-3 draw courtesy of a 98th-minute equaliser after Everton themselves had taken the lead in stoppage time.
Lukaku did finally break his duck against Chelsea in the FA Cup sixth round later that season, though, scoring twice in five second-half minutes to fire Everton into the semi-finals at Goodison Park.
Neither Lukaku nor Everton will remember last season's meetings too fondly, with Chelsea scoring eight goals without reply in their two games against the Toffees.
Romelu Lukaku's record vs. Chelsea
Home goals: 2
Away goals: 0