The 26-year-old’s Red Devils future is in doubt after enduring a difficult second season at Old Trafford
The former Chelsea, West Brom and Everton striker fell out of favour under new boss Ole Gunnar Solskjaer in the second half of the 2018-19 campaign with England international Marcus Rashford being preferred.
The 26-year-old ended the season with 15 goals in 45 appearances for United in all competitions. That represents a considerable drop from the 27 goals he scored in his debut campaign at the Red Devils following his £90million move from Everton in the summer of 2017.
Now his international boss Martinez, who also managed Lukaku at Goodison Park, has stressed the importance of Belgium's leading man finding a new club.
"It is clear that he has to leave Manchester United," Martinez told Belgian outlet Het Laatste Nieuws.
"It would be a good thing for both parties. It is now important that Romelu finds the right club."
Belgium's record scorer Lukaku, reportedly valued at £80million by United, scored three goals for Martinez's men across two Euro 2020 qualifiers earlier this month.
The striker began his career at Anderlecht before moving to Chelsea as an 18-year-old in the summer of 2011.
Lukaku struggled for regular senior football at Stamford Bridge so was sent out on loan to West Brom, where he scored 17 goals in 18 appearances in the 2012-13 season.
He moved to Martinez’s Everton on another season-long loan the following year, with the Toffees sealing a permanent £28 million move in the summer of 2014.
Lukaku scored 87 goals in 166 appearances in all competitions for the Merseysiders, becoming the club’s record Premier League goalscorer in the process, prompting United to bring him to Old Trafford two years ago.