The 22-year-old has netted 12 goals for the Tractor Boys this campaign, but he is expected to depart at the end of the season.
There is a £30 million relegation release clause in his contract and both United and Chelsea seem prepared to activate it.
Delap spent many seasons in the youth ranks at Manchester City and he would prefer a return to familiar surroundings next term.
Hence, United have the upper hand over Chelsea in the race and their prospects could be boosted with Champions League football.
The Red Devils take on Tottenham Hotspur in the Europa League final later this month. A victory would secure a Champions League berth.
Delap has his sights on playing European football. He could decide his future after what happens to United in the final at San Mames.
There is a possibility that United could still win the race for him.