The American has insisted the striker will stay at Anfield this summer, and he will continue to refuse offers from rival clubs as he is keen to qualify for the Champions League
Arsenal have seen two bids for the Uruguayan rejected - the latest being £40,000,001 in an attempt to trigger a supposed release clause - but the Reds chief has described the prospect of selling their star man as "ludicrous".
Brendan Rogers, who has consistently backed Suarez despite a string of controversies, has now accused the player of "total disrespect" and ordered him to train away from the first-team squad - a decision backed by Henry after criticising the club in an interview with The Guardian on Tuesday.
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"For all the top clubs it's extremely important [not to sell to a rival] but especially for Liverpool because we're not in Europe this year and have not been in the Champions League for a while.
"To sell to a rival for those positions, or one of them, would be ludicrous. Liverpool needs to be playing in Europe, it needs to be playing in the Champions League, that's what Liverpool football club is about.
"I'm unequivocal that we won't sell to Arsenal, whatever the bid is. I have not said it to Stan [Kroenke, Arsenal's majority shareholder] but I had a personal conversation with others at Arsenal and told [chief executive Ivan Gazidis] we would not sell to Arsenal.
"He won't be sold even if a foreign club comes in because we do not have time to sign a suitable replacement.