Brendan Rodgers revealed following Liverpool's 2-1 victory at Anfield that he received a text from the striker on Sunday morning.
"Luis Suarez sent us a lovely text this morning, wishing us all the best and telling us to start strong - it's a lovely gesture," said Rodgers.
"He sent the text to me personally. What did it say? Don't be so nosey! I texted him back. It's a great love-in I've got with him!
"He's a great boy, but he's gone. It was a lovely touch. Liverpool will always be in his heart."
Suarez was Liverpool's top scorer last season with 31 league goals, but he was sold to Barcelona last month after being given a four-month ban by FIFA for biting Italy's Giorgio Chiellini at the World Cup.
It was the third such incident of the Uruguayan's career.
Daniel Sturridge, Suarez's former strike partner, scored Liverpool's winner against Southampton, but Rodgers said that he would look to bring in another striker before the transfer window shuts on September 1.
"We're bigger than any one player," Rodgers said, in reference to Suarez's departure.
"I still think we need a striker, so we'll search through until the end of the window for that."
Suarez could make his Barcelona debut in a friendly against Mexican side Leon on Monday, after the conditions of his suspension were relaxed by the Court of Arbitration for Sport.