Liverpool chairman Tom Werner believes Suarez can play regular Champions League football by staying at Anfield.
Suarez was involved in intense speculation over the course of the summer with reported interest from the likes of Real Madrid and Arsenal.
The Uruguayan, who recently returned from a ten match ban, has been in scintillating form scoring three times in two Premier League games so far.
The 26-year-old expressed his desire to play Champions League football during the transfer window, paving the way for a move to Arsenal following a £40 million-plus bid from the north London club.
Despite trying to force a move through in the summer, Werner admits it was important that the Red's managed to hold on to their prized asset.
Werner told Sky Sports: "There was interest in him from other clubs throughout the summer but it was important for us to try to keep him.
"He is one of the great players of the world and we felt that we would be a stronger club with him than without him.
"That does not mean I don't respect his intense desire to play in the Champions League. But it would be a very happy day next May if and when we get to the Champions League by finishing in the top four and he is part of it.
"It is our intention to keep him for a while. Our intention is to build a winning club and he is integral to that.
"The past is the past and I have great affection for him personally."
Liverpool currently sit level on points with Arsenal at the top of the table, after a 3-1 win against Crystal Palace last week.
Werner was keen to praise the work done by Liverpool boss Brendan Rodgers during his time in the Anfield hot seat.
"I think Brendan has made remarkable progress," Werner said in the Daily Mirror.
"He's a great strategist and has shown strong leadership. When we hired him, we were confident we were getting one of the brightest managerial talents in the game and he is proving his worth.
"He's dedicated to improving the club as a whole and shares our vision of developing a club that is built for sustained success.
"He has shown a willingness to use young players and at the same time, demonstrated the ability to get the best out of our established stars.
"Brendan is respected by the players. They feel he is a good strategist and a good leader and his philosophy has been embraced by everyone.
"We are all moving in the same direction and Brendan is very much the leader.
The Chairman is also happy with the progress the club is making off the pitch, and hopes the Red's can consistently compete for silverware in the future.
"We're pleased with the progress we're seeing on the pitch but our goal is to create sustainable, long-term success at Liverpool and to consistently compete for silverware, so we're not getting carried away with a few good months.
"The club is definitely moving in the right direction under Brendan and as owners we're very optimistic and excited about the future."
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