Rumor hats on people, this is about as cheesy a source as they come. According to an anonymous tipster, David Tennant has been approached by Warner Bros for a possible role in Justice League movie. What character would he play? Well, according to this guy... Plastic Man? Yeah, can we just disregard this report?
The rumor started with a user named Jet Beetle on TheRPF Forum, who claimed he was in touch with a couple of the producers on JL.
"A couple of producers I know told me they were involved with the upcoming Justice League movie -- I've known these guys for years and as nice as they are they have never been involved with something as big as JL, so who knows. They did say Warner is basically trying to follow Marvel's lead (no surprise there) and amongst the heavy hitters already expected to be on hand (Superman, Batman, Wonder Woman, Aquaman) they want to put in a comic relief character (they seem to believe this is what Ant Man will be - no matter how much I defended the character I had to admit I had no idea how Pym will be handled in this upcoming film). Then when they told me the character Warner was planning to include.... well, I smiled and could totally see it as a good thing. The idea of Plastic Man bouncing all over the place and the fact that the studio is looking at David Tennent to bring him to life."
So obviously consider this rumor with truckloads of salt. In fact, let's go with all of the salt in the world. Hell, entire alternate universes where everything is made of salt. Yes, let's try that.
While The Doctor would be an awesome inclusion in any superhero movie, Plastic Man seems just a little too far fetched. And besides, Tennant was rumored to be up for the role of Rocket Raccoon in Marvel's Guardians of the Galaxy, and look how that turned out.