The Catalan club claimed Suarez was “100 per cent” their player last week but there has not yet been an official announcement from either club.
The controversial striker is currently going through an appeal to the Court of Arbitration for Sport against his four-month ban from football, including nine international matches, for biting Italy's Giorgio Chiellini at the World Cup.
But Rodgers once again spoke about Suarez in the past tense from Liverpool's pre-season base in Boston and hailed the man who scored 33 goals in 39 appearances for his side last season.
“Luis hasn’t let me or the club down at all - he gave everything for Liverpool,” Rodgers said.
“Of course there have been issues, but they’re in the past. He was a brilliant player for us and for me, and I will always see him as a good man and a good friend.
“It’s a shame he’s not here but Liverpool, as a club, is bigger than any individual and we will move forward without him.
“It’s really exciting going into this season. We’ve qualified for the Champions League and brought in some good players. Hopefully we’ll progress.”
Rodgers was speaking at his first press conference in the USA, having been taken ill when the club touched down in Massachusetts on Tuesday.
Their arrival followed the announcement by Liverpool captain Steven Gerrard that he was retiring from England duty and Rodgers believes that decision will be beneficial to his side’s hunt for silverware this season.
“I’ve spent a lot of time speaking with Steven and I know how much it means to him to play for and captain England - he was a wonderful captain,” the Reds boss said.
“But Liverpool means everything to him and there’s certainly no doubt missing out on international football means he will be fresher and at his optimum level as often as possible for us.”