Schaars, 28, joined Sporting from AZ Alkmaar last summer for just over £1million but could fetch many times that amount for the Lisbon club when the transfer window opens again in June.
Fulham and Sunderland have been watching Schaars this season and will have been impressed by his display again last night as Sporting grabbed a 2-1 first-leg lead against Athletic Bilbao in the Europa League semi-final.
The left-footed Dutchman, who has been capped 16 times by the Netherlands and is in contention to make their Euro 2012 squad, has scored three goals this season and also started for Sporting in their 1-0 win over Benfica earlier this month.
Fulham boss Martin Jol knows Schaars well from his years in Holland while Martin O'Neill is also on the lookout for a central midfielder and may have been impressed by his display as a second-half substitute against England at Wembley in March.
Fulham last week