The Belgium international is on-loan at Roma this season from AC Milan and has shone with the Giallorossi.
However, Saelemaekers' future is undecided, with his Roma deal not carrying a permanent option.
Il Corriere dello Sport says Newcastle United and Nottingham Forest are interested in Saelemaekers ahead of the summer market.
And Milan would be willing to sell at a starting price for €25m.
Any move from either Premier League club would hinge on qualifying for next season's Champions League.