The England manager is looking at a number of players who are eligible for the Three Lions, including West Ham's Irish star Declan Rice.
Nottingham-born Cairney, 27, has a Scottish father and English mother so is eligible to play for both countries.
Even though he has played twice for Scotland, they were friendlies against Canada and Costa Rica.
Cairney, who joined Fulham from Blackburn in 2015, is aware of England's interest.
He has frustrated Scotland by repeatedly pulling out of squads, citing injury, with his last appearance coming against Costa Rica in March.