Toffees striker Lukaku has been linked with a summer move to Old Trafford.
Lukaku has been heavily linked with a summer move to Old Trafford, which would leave the Toffees with a significant void to fill.
The Belgian has scored 25 goals at club level this season, and 61 in 119 appearances for Everton, but Janssen - who's found the net 20 times in his first season in Holland's top flight - could be the ideal candidate to replace him.
Janssen's form led to a first international call up last month, and he impressed on his first start - scoring and assisting in the Netherlands' 2-1 win against England at Wembley.
But United's attention may also have piqued at Janssen's recent performances, and the 21-year-old is likely to cost far less than Lukaku, for whom Everton paid £28 million two summers ago.
Should the Red Devils fail to qualify for next season's Champions League, they risk losing out on Lukaku to Juventus, Paris Saint-Germain or Real Madrid, who were all listed as suitors by the Times last week.
And PSG are also said to be circling around Janssen, according to De Telegraaf.