The 19-year-old defender starred at centre-back as Rovers established themselves as surprise leaders of League One, but an abductor injury has curtailed a loan spell that was due to end in January.
Gibson was rewarded with a new four-year contract on his return to Teeside this week, and Moore is confident a deal can be done for him to boost to Tranmere's promotion push when he is back to full fitness.
"He's desperate to come back and we're desperate to have him," said Moore. "He's been absolutely fantastic for us and I'd like to think that we have been for him.
"He's signed a new four-year contract at Middlesbrough so I'd like to think that's obviously (because) he's proven he can play at this level.
"I would imagine that Tony (Mowbray, Middlesbrough boss) is going to push him more next season to get him into that side.
"We'd like to bring Ben back until the end of the season, there's no doubt about that, and the boy wants to come."