Newcastle United are 7/2 to sign the Hull City man and reported Liverpool target.
Rafael Benitez's side are gearing up for their return to the Premier League after winning the Championship last season.
The Magpies have only secured the permanent signing of Christian Atsu so far, despite a lot of speculation about a lot of players, but there has been no rumours about the 23-year-old.
Nevertheless, Sky Bet have installed Newcastle as 7/2 third favourites to sign the Scottish defender.
Liverpool (3/1) are narrowly ahead in the betting, while Burnley (10/11) remain odds-on favourites to sign the highly-rated full back.
The Mail reported in May that Liverpool were closing in on an £8 million move for Robertson, though these claims appear to be wide of the mark given that he has not yet joined the Anfield club.
But HITC Sport claimed this week that Burnley had bid to secure his services, but it remains to be seen where his future lies. Given how Hull were relegated last season, it appears unlikely that he will be at the KCOM Stadium next term.
Liverpool have James Milner and Alberto Moreno as left-back options, though the Spaniard is expected to leave Merseyside. Newcastle, on the other hand, only really have Paul Dummett and Achraf Lazaar for that role following Vurnon Anita's release.
Liverpool's James Milner celebrates scoring their second goal