The Gunners made a £40,000,001 bid for the Uruguay international in the belief that would trigger a clause in his contract which was instantly rejected.
Suarez went public with his frustrations by claiming the club had reneged on a deal he claimed allowed him to join a Champions League side.
It made little difference as principal owner John Henry was adamant there would be no sale.
"I understand why Arsenal would want to buy a player of Luis' quality because he is one of the leading strikers in the world but it was something that was never going to happen," said Rodgers ahead of the trip to the Emirates Stadium.
"For us and the institution we are we certainly weren't going to sell to a rival, a competitor, and that was something which was very strong from the off.
"There was all sorts of gossip on the summer but we were very firm in our leadership, from the top right the way through, that this was something we didn't want to do.
"It was a great credit to the owners and the leadership of the club that they stood by what my thoughts were as a manager and they backed it all the way."
Third-placed Liverpool will be looking to strengthen their top-four credentials against the Gunners in the evening kick-off after a good start to the campaign.
That has left Rodgers insisting Suarez can fulfil his Champions League ambitions without leaving.
"There is no greater stage for him than a club like this," added the Northern Irishman.
"He is a player, like some of our other players, who deserves to be playing at the highest level of European football but we believe he can do that at Liverpool.
"We won't get carried away, we have to keep our concentration and continue to work very hard."
Liverpool go into the game on the back of the resounding 4-1 home win over West Brom, which saw Suarez score a hat-trick to make it six in five league matches since returning from suspension. Daniel Sturridge scored the other to take his tally to eight in nine - having failed to score against only Southampton in the league this season.
Rodgers will be boosted by the return of playmaker Philippe Coutinho, who is back after missing more than six weeks after a shoulder operation. Left-back Jose Enrique is still troubled by a knee injury, however.