Experienced midfielder Livermore, in the final year of his contract at The Hawthorns, has struggled for minutes under head coach Carlos Corberan.
His last Championship start was in the Spaniard's first match in charge, where he played less than an hour of the 2-0 defeat to Sheffield United.
Winger Wallace, though, who has been a big hit in his debut campaign, insists nobody has a bad word to say about the captain due to his relentless support.
Wallace said: "You’ve got people like Jake (Livermore), Barts (Kyle Bartley) and Matty Phillips who have been here for a long time.
"Jake especially. He’s not been as involved as much as he would have wanted to have been recently but he still travels to all the away games himself and is in the dressing room before games with us all.
"These are the things that the fans don’t see. That’s the reason when you ask around in football that you won’t find anyone who has a bad word to say about Jake. He’s a great person to have in the dressing room supporting the lads.
Wallace explained 33-year-old Livermore's encouragement behind the scenes is a crucial factor in setting standards. He added: "I’ve played with lads who when they’ve not been playing perhaps don’t want the team to do well. He’s someone that every time we win, he’s the first one at the door when we’re walking back into the dressing room giving all the lads a hug. He makes sure we’re at it every week."