The Northern Irishman says the Barcelona striker wanted to show his continued support of the Reds - despite his summer switch to Camp Nou
The Uruguay international left for Barcelona in the summer after a traumatic World Cup that saw him banned from football for four months for biting Giorgio Chiellini during his country's 2-1 defeat to Italy.
Suarez's ban has subsequently been upheld by the Court of Arbitration for Sport (CAS), although he is now able to train with his new club.
However, despite all of the drama of the past few months, Rodgers says that Suarez has not forgotten his former colleagues.
“He sent me a lovely text this morning wishing us all the best and telling his old team-mates to start strongly," the Northern Irishman told reporters. "He’s a friend of Liverpool now.
“I sent one back. He’s a good boy but he’s gone. His heart is with Liverpool. He’ll always be Liverpool and it was a lovely touch."
Liverpool beat Southampton 2-1 in their opening Premier League game, with Raheem Sterling and Daniel Sturridge on target for the Reds, and while Rodgers was not too impressed with his side's performance, he was thrilled with the three points.
"I think pre-season was broken with players coming back late. We had to grind out a result," he added.
"Today was a brilliant win for us. It was a tough game and we had to grind it out so I’m really happy with the determination and character. As the season rolls on we will play better.
"You know you want to make a good start and get going. We weren’t as fluent, it was all about the win and the victory.
"Southampton are a good side with some very good players. We had to show guts and determination. We put Rickie [Lambert] on and changed the way we played. I think that unsettled them a bit."