The Sun says the billionaire Chelsea owner has so far stayed out of the contract row between the club and its two England stars.
But with midfielder Lamps and defender Terry at loggerheads over new deals, Abramovich has now asked Blues chief executive Peter Kenyon to resolve the issue once the players return for pre-season.
There is still work to be done though to repair the damage done to the relationship between the club and its skipper and vice-captain.
Terry feels he has not been shown the respect his performances and commitment to the club deserve.
Lamps feels the same and is disappointed the situation has not been sorted out before now.