The 27-year-old is ready to leave Sunderland on loan in order to get regular first-team football.
Kilgallon has failed to make the expected impact at Sunderland since joining the club from Sheffield United.
“A few Championship clubs are looking at Matt, although I do not want to say who they are at this stage,” said Kilgallon’s agent Paul Masterton.
“There is a good chance something will happen this week.
“It has been a very difficult time for Matt because he is not playing at Sunderland and that does not look like changing for the time being.
“He just wants to be back playing again, and a loan move would be the best option for him at the moment.
“He has not given up on Sunderland but he does need to play games somewhere.”
