The Uruguay international, who is trying to force his way out of Anfield amid interest from Arsenal, received the support of Liverpool after he was found guilty of racially abusing Manchester United's Patrice Evra.
The Premier League outfit also stood by the prolific striker after he was caught biting the arm of Chelsea defender Branislav Invanovic, resulting in a 10-game ban.
"I think he does [owe Liverpool] and everyone in their correct mind would see it like that," Souness told Sky Sports News. "I think back to the T-shirts at Wigan when he got himself in real bother and the Ivanovic situation last season.
"The board have stood by him, the club have stood by him and the manager has stood by him. You would like to think a bit of common sense and loyalty would prevail but that doesn't appear to be the case."
Suarez has been ordered to train away from his teammates.