Suarez, banned for 10 matches after biting Chelsea defender Ivanovic during a Premier League clash in April, has expressed a desire to leave Anfield this summer.
He has previously laughed off talk of a switch to Chelsea but Stamford Bridge continues to be mentioned as a possible destination and Ivanovic has indicated that he would be happy to play alongside Suarez.
"About Luis Suarez, I said straight after the game, whatever happened on the field finished there," Ivanovic said in Bangkok on Tuesday.
"He's one of the best strikers in the Premier League. I don't have any problem with him."
Ivanovic has been linked himself with a move, with big-spending Ligue 1 clubs Paris Saint-Germain and Monaco reportedly courting the Serbia defender's signature.
The 29-year-old downplayed the prospect of a transfer ahead of Jose Mourinho's first match of his second spell in charge, the Bangkok clash with Singha All-Stars which comes a week into pre-season preparations.
"The first thing, we are a little bit too far from reality," Ivanovic said.
"We are not so focused on that kind of thing.
"For us, the most important thing is to pass this base, which is very important for every single player for the beginning of the season.
"My situation, I've always said I'm happy to be here.
"I will do everything and will work hard to do everything for the club. Nothing will change until the last day I'm here."