Leeds tried to sign De Paul from Udinese during the last transfer window and have continued to be linked with him, while Liverpool are also now claimed to be in the race.
However, the Premier League duo could be in line to miss out on the acquisition of the midfielder, with Inter poised to land the player from their league rivals.
According to Italian daily Tuttosport, the Nerazzurri could complete the signing of De Paul from Udinese in the summer, but have not ruled out the possibility of landing him during this month’s transfer window.
Antonio Conte’s side could snap the Argentina international from Udinese up this month if they sell Eriksen before the end of the window.
The Dane’s move to Inter from Tottenham last year has not gone according to plan and the Serie A outfit are open to moving him on this month.
A return to Tottenham has been touted for Eriksen but Inter, who paid around £24m for his last year, could be forced to accept a loan departure.
A loan move would be unlikely to bring forward an early swoop for De Paul and Inter need to sell Eriksen to make space for the Argentine.