By Sarah Spina-Matthews
Copyright bbc
He continued: “Obviously, I do watch what is going on down there, so I’m not going to say not.
“This is the thing I want to get over to people – it wouldn’t be me saying ‘right I’m going to put myself right out there again’.
“It would have to come in a different direction of people.”
Burham is not currently eligible to stand to be Labour leader because he is not an MP, but there has been media speculation he could run in a by-election.
He denied being the source of the speculation, saying: “I’ve not put the stories on the front pages.
“Other people did that for reasons best known to them.”