According to sources, the couple met at a charity gala event in LA two weeks ago, where they looked very happy together in photographs.
The 52-year-old actor, who is divorced from actress Robin Wright, met the 26-year-old at the Gucci event and according to party goers, he was “flirting with her all evening” and asked to see her again.
Welch is single since splitting with her partner last September and Penn is also unattached, having very publicly dated ‘Lost in Translation’ star Scarlett Johansson following his marriage breakdown.
According to sources he ended things with the actress because he “didn't want anything serious”.
He has two children from his 12-year marriage to Robin Wright.