"I think everyone is, even Gareth himself probably. We are looking forward to doing well for him and fighting for him over the next two games," Lallana told British media when asked if he was keen on a quick resolution to the managerial situation.
Southgate was promoted from the under-21 set-up for a four-match run after Sam Allardyce parted ways with England after just one game in charge in September when he was caught seeking a lucrative sideline role in a newspaper sting.
"You need stability. What you don't have at England is the time that you get at club level," the Liverpool midfielder added.
"You can't prepare for a campaign as you would for a league over the course of the season. It's not possible, so it's a different challenge.
"I'm sure Gareth will want to take on that challenge and we are ready to fight for him in the matches. Hopefully, he will do well enough to get the job on a permanent basis."
Lallana, who is part of the England squad for Friday's World Cup qualifier against Scotland and a friendly against Spain next week, said a possible identity crisis within the side could have contributed to the team's recent international failures.
"It would be nice for Gareth and for us to know quite soon whether he's going to get the job on a permanent basis, so you can build towards having a certain identity that your manager wants you to have," he added.
"That's what a manager is there for... For quite a few years now we've not done brilliantly at major tournaments, so it's up to us to maybe find an identity."
(Reporting by Shravanth Vijayakumar in Bengaluru; Editing by John O'Brien)
