This is according to talkSPORT, who suggest that the Serie A outfit could go on to test Basel, who are expected to sell the £7 million-rated centre-back following the conclusion of the 2013/14 campaign.
News of Lazio's efforts in this regard will presumably alarm both aforementioned Premier League giants, with Manchester United and Arsenal each having been interested in Schar for several months now.
The departure of inspirational captain Nemanja Vidic to Inter Milan - confirmed during the reign of former boss David Moyes - this summer will leave Manchester United desperately short of cover at the back and it will be up to the club's next permanent manager to resolve that particular issue.
Arsenal boss Arsene Wenger, meanwhile, appears to have settled on a regular defensive pairing in the shape of Per Mertesacker and Laurent Koscielny, with the duo having impressed with their solidity and ability to compliment one another nicely throughout the majority of the season.
However, with major doubts continuing to hang over the futures of both Bacary Sagna and Gunners skipper Thomas Vermaelen, it could be that Arsenal are also on the lookout for adequate reinforcements at centre-back before too long.
At 22, Schar has already made five international appearances for Switzerland as well as proving his ability and maturity on the domestic stage with Basel.
Additionally, the former FC Wil 1900 starlet - who represented his country at the London Olympics in 2012 - has proved a steady performer on the European stage, having appeared for his club on numerous occasions in the Champions League.
If Manchester United and Arsenal do indeed harbour ambitions of signing Schar, then it looks like they could face a significant battle with Lazio lurking.