Martin and Paltrow, 42, announced separation in March and have since remained friends. It is said that Martin, 37, and the Oscar-winning actress, 24, have been dating from past two months.
Paltrow wants to get to know the 'Hunger Games' star and thinks they would get along, reported Us magazine.
"She'd like to spend a little time with her and thinks they'd probably get along," an insider said.
The source added that the 'Shakespeare in Love' actress is 'fine' with Martin's apparent closeness to Lawrence but would like him to wait a bit before introducing her to their kids, daughter Apple, 10, and son Moses, 8.
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