Former Reds star and Inter Miami striker Suarez has long been an adviser to Nunez - and they remain in touch.
"Yes, we always talk. Luis always shows up when things are going badly," Nunez told TNT Sports Mexico.
"He doesn't like to appear much when things are going well. And that says a lot about him, about his character and quality as a person. Whenever we can, we chat a bit about football and life in general."
Nunez struck against Southampton on Saturday to spark a come-from-behind 3-1 win.
"First of all, I'm very happy. I'm happy for the team that has been doing things well," he said. "Today it was a bit tough to get the three points, but we managed to pull through.
"We need to keep going; this isn't over yet. There are many matches ahead and we all know the Premier League is very difficult, but we have to keep working."