Jurgen Klopp's side face Hoffenheim in Germany on Tuesday night in the first left of their Champions League play-off and Thompson believes that losing is not an option for the 'Reds'.
Speaking to 'Sky Sports' ahead of the game, the 63-year-old said: "I think the outcome of the play-off could have a knock-on to Coutinho; if things go pear-shaped then has a pretty good excuse to say, 'Let me go, I want to play in the Champions League', so it is even more important in that respect.
"If we get through to the group stages then I think the owners - because they put everything at Coutinho's disposal before, giving him a five-year deal and the pay increase that he and his agent asked for - have strong enough grounds to stand firm.
"The owners know it's Barcelona but to them it's a contract signed and until they've got a player who can fill his boots then they have no interest in selling, especially after the way the club was embarrassed with the timing of the transfer request."
The former England international also admitted that Liverpool are in for a tough test against the Germans, saying that it was the most difficult tie possible for the Merseysiders.
"Out of all the teams we could have played this was the hardest. We could have had Nice, Steaua Bucharest, Young Boys or Istanbul BB and we pulled out Hoffenheim. They are very good defensively, very good at set-plays and Liverpool obviously need to improve at the back," he explained.