Santorum and Lohan: Rick to Lindsay Lohan -- Pose for Me!

Former presidential hopeful Rick Santorum did not take a photo WITH Lindsay Lohan last night -- but sources at the White House Correspondents' Dinner tell TMZ ... he took one OF her.

According to our sources inside the party, LiLo was sitting with Fox News personality Greta Van Susteren when Santorum came up to say hello. We're told Lindsay was asked to take a picture of him with Greta using his camera, which she did.

Then ... our sources say Rick asked to take a photo of Lindsay using his camera. Yes ... of just Lindsay.

We're told Lindsay smiled and obliged and Santorum then went on his way.

Our photog asked Rick about the picture after the party ... and he played dumb about the photo.

He might not be running for President any more, but he can't take any chances.