SunSport understands the Northumberland whistler, 31, has attracted interest to officiate in the American MLS.
The news comes just 48 hours after Mark Clattenburg quit the Prem in a shock switch for Saudi Arabia.
Top Prem refs are becoming increasingly disillusioned with the refs governing body and chief Mike Riley.
It is believed morale among Select Group One officials is at an all-time low.
News of the interest in Oliver is commonly known within top refereeing circles.
And that feeling of discontent could lead to even more elite refs moving away from the top-flight.
Ex-top Prem ref Howard Webb has taken a new role – starting on March 1 – in the US to initially help with the game’s development of video assistants.
But it is understood that Webb will eventually become head of referees for the MLS this summer, replacing Peter Walton.
And Oliver is viewed as the number one target to officiate games in the top-flight Stateside.
Refs governing body Professional Game Match Officials Limited (PGMOL) are already preparing for the future following the shock loss of Clattenburg mid-season.
Select Group Two refs David Coote, Chris Kavanagh and Andrew Madley, brother of current Prem ref Bobby, have been promoted with immediate effect.
While Lee Probert, who last refereed a Premier League game in May 2015, has also finally passed his fitness test following a back injury – nine months after the other officials in the elite group.
As a result, three refs from the National League have been invited to train with the select group two officials.