Italian media outlet Rai Sport, as quoted by Metro, is reporting that the Red Devils are eager to sign the Brazil international.
The same article states that the Red Devils hierarchy have discussed the proposed transfer with interim Manchester United manager Ole Gunnar Solskjaer.
According to the same story, Manchester United could find it tough to sign the South American forward from Juventus given that the Italian giants are reluctant to sell.
The report adds that Juventus value Costa at around £70m, which is significantly less than the £54m offer Manchester United are thought to have made.
Juventus, according to Rai Sport, are interested in re-signing Paul Pogba after the Serie A side sold the versatile midfielder to Manchester United in an £89m deal in 2016.
However, France international Pogba could be set for a new lease of life at Old Trafford after Manchester United parted company with their manager Jose Mourinho last week.
Manchester United have won their last two Premier League games since Solskjaer took over the reins from Mourinho ahead of their trip to Cardiff in the Premier League.
The Red Devils were 5-1 winners against Cardiff in their final game before Christmas Day before a victory over Huddersfield Town on Boxing Day.
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