The centre-back, 20, impressed during a spell on the Wirral earlier this season, making 25 appearances in all competitions.
Moore was due to watch Gibson play for Boro's Under-21s this week before a minor knee injury ruled him out, but the Rovers boss remains confident a deal can be done.
"Ben was supposed to play for their Under-21s on Monday but jarred his knee in training on Sunday," he told Tranmere's official website.
"The shout is it's not too bad and hopefully he'll be back here for our physio to have a look at him and join in on Monday next week."
