Straczynski is a noted Doctor Who fan of many decades' standing, having watched the show when it aired on PBS in the United States in the 1970s. Straczynski, a self-confessed Anglophile, was also a massive fan of The Prisoner and Blake's 7, and has frequently cited all three as influences on his classic space opera series Babylon 5.
Straczynski has also cast Doctor Who alumni on his showers: Guy Siner (Genesis of the Daleks) appeared as a Minbari on Babylon 5 and Christopher Neame (Shada) was a "Knight" on the same show, whilst Sylvester McCoy (the Seventh Doctor) and Freema Agyeman (Martha Jones) appeared on his later Netflix series Sense8.
Doctor Who has traditionally always been headed up by a British showrunner, although its original creator Sydney Newman was Canadian and the show's second showrunner (though the term did not exist back then), John Wiles, was South African. Even the producer in charge of the 1996 American Doctor Who TV movie was British, Philip Segal.
Furthermore, even if the BBC were willing to look beyond Britain for a new showrunner, they seem to have a specific antipathy towards American writers. Acclaimed SF and horror novelist Joe Hill pitched three scripts to Doctor Who with the help of Neil Gaiman and received a shocking reply from the BBC saying, "We have never let an American write Doctor Who, and if we were going to, we wouldn't start with you."
So the chances of Straczynski being considered for the role appear to be slim, despite the fact he's a very popular choice among both fans and more general viewers and would tick the boxes of being a strong SF writer of great experience, a very experienced showrunner and also a writer noted for tackling wide-ranging and diverse subject matter. It seems more likely that the BBC will be looking for a British (or, at the very least, non-American) producer instead.