The Premier League trio all watched the Italian side's 1-0 victory over Verona earlier in the month.
The 23-year-old only moved to the Serie A club from PSV Eindhoven in the summer, but the Premier League trio appear to be considering attempting to lure him away, having watched him during the Rosanero's narrow 1-0 victory over bottom side Verona earlier this month.
Hiljemark's performances have been one of the major factors behind Palermo keeping themselves just above the relegation zone this season. Only veteran forward Alberto Gilardino has scored more than the three league goals that the Swede has managed. And he has backed up his goals with two assists.
His vision and passing ability is likely to appeal to the three clubs looking to bring him to England, as he has often proved that he is able to see a run and subsequently pick out a pass that unlocks the defence.
Sky Sports reports that the midfielder has also been linked with AC Milan and Napoli, which may tempt the three English sides to make a move in the near future as it could become difficult to compete with the two Serie A giants, should they enter the running for his signature.