Tigers vice-captain Allen suffered a freak injury to his calf in the game against Northampton Saints at Welford Road in October which required surgery to remove a blood clot and relieve pressure in the muscle.
He has been working with the Tigers medical team on his recovery, and director of rugby Richard Cockerill says he is making very good progress.
“Anth is getting close to being fit,” Cockerill said. “We’re taking it week by week but he is improving a lot.
“The physios have done a great job, Anth is a great professional and great athlete. Hopefully in the next few weeks he should be back to playing.”
Supporters saw Allen and hooker Hawkins, on his return from a shoulder problem which resulted in surgery during the summer, join the team's warm-up ahead of Saturday's win over Sale Sharks at Welford Road.
Tigers have been hit hard by injuries in the first half of the season but Cockerill received some other good news when it was confirmed that centre Matt Smith had not broken a thumb again during last week’s match against Saracens.
Smith missed the opening months of the season after breaking the thumb in pre-season training and there were initial fears he had suffered the same injury at Allianz Park.
“It’s not broken, he’s had a check on that,” said Cockerill. “It's the same thumb but it seems it’s just heavily swollen and he's able to play.”
Mathew Tait made his first appearance of the season in the match at Saracens after recovering from an ankle injury, and prop Logovi’i Mulipola is recovering well from a calf injury suffered during the autumn Test for Samoa against Ireland.
Manu Tuilagi, Geoff Parling and Tom Croft are still sidelined by long-term injury,
“We’ve been missing a lot of guys and those long-term injuries are to guys in important positions,” said Cockerill. “But they’re in good hands with the medical team and we’ll get them back at some point. You have to trust your squad over the course of a long season.”