Lescott played a key part in Manchester City's title-winning side two years ago, but he has struggled to gain a regular first-team spot ever since.
Nolan spoke to Lescott after their Capital One Cup semifinal on Tuesday.
"I was trying to tell him to come and help us out," said Nolan, whose friendly exchange with Lescott was picked up by the television cameras.
"I saw Joleon and I know he has been heavily linked with us and I was trying to persuade him (to come to West Ham) because he is a top-quality player. That would only make us stronger."
It remains to be seen whether Lescott, who is out of contract this summer, would be interested in a move from a title contender to Upton Park, though.
Nolan jested that the initial signs were not good.
"When I said that to him, he laughed and said: 'You're joking aren't you?"' the former Bolton midfielder joked.
"I'm only winding you up," he added. "He didn't really say that, but we did have a little bit of laughter and a giggle."
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