Left-back Tierney has been strongly linked with a move to Arsenal, who have failed with two bids for the 22-year-old.
Transfer consultant Ian McGarry has suggested Robertson urged his Scotland teammate to leave Parkhead for the betterment of his football.
"Having won the Champions League at the end of last season, he's told Tierney 'look, don't default your career for the sake of staying at the club you support'."
But Scotland skipper Robertson took to Twitter on Monday to distance himself from McGarry's suggestion, tweeting an article about the subject with the post "lot of rubbish".
Lot of rubbish https://t.co/TYlzTNyA7o
— Andrew Robertson (@andrewrobertso5) June 24, 2019