Suarez is eager to leave the Anfield club and said earlier in the week that he had been promised he would be sold if Liverpool failed to qualify for this season's Champions League, while Arsenal have bid £40million plus one pound for the Uruguay forward.
But outraged Liverpool boss Brendan Rodgers denies any promises were made, has accused Suarez of lacking respect for Liverpool, and has banished him from training with the first team.
And Henry, the leader of the Boston-based Fenway Sports Group that owns Liverpool, says Suarez will definitely not be allowed to join a rival Premier League team.
"We are not going to sell Luis," said Henry.
To sell would be ludicrous
"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."
And Henry says even an increased bid from Arsenal will not change his stance.
"I'm unequivocal that we won't sell to Arsenal, whatever the bid is," he said. "I have not said it to Stan (Kroenke, Arsenal's majority shareholder) but I had a personal conversation with Ivan Gazidis (Arsenal chief executive) and told him we would not sell.
"He won't be sold even if a foreign club comes in, because we do not have time to sign a suitable replacement.
"It's a football reason, it's not about finances. That's why, at this point, so late in the window, with everyone who's already moved or isn't moving, we can't replace him. So, for football reasons, we can't sell, and especially to Arsenal."
And Henry does not believe that Suarez's relationship with Rodgers and the Liverpool fans has been damaged beyond repair.
"The manager is upset, as he should be, and the supporters are upset," said Henry. "But we need Luis. Hopefully this will pass."