The 22-year-old has had a good debut campaign in the Premier League with Ipswich Town. He has registered 12 goals alongside a couple of assists.
He can be signed for just £30 million after Ipswich's relegation and reports claim that he would prefer to join United over the Blues this summer.
Delap spent several years in the academy ranks at Manchester City and he is keen on returning to the north west ahead of the 2025/26 campaign.
Hence, United have an upper hand in the race, but they still need to qualify for the Champions League to persuade the striker into a transfer.
As things stand, league counterparts Chelsea are on course to make the Champions League next season through a top-five league finish.
United's prospects depend on winning the Europa League final against Tottenham Hotspur. It won't be a straightforward task for them.