The 25-year-old England international underwent hip surgery in New York in May Tuesday in an attempt to cure a number of related problems with his thigh and calf which restricted him to just eight Premier League starts last season.
After his operation, September had been the likely date for him to reutn to training - instead, ESPN reports that the forward will get back in training in the next few weeks and could be ready to start against United at Old Trafford on September 12.
Sturridge has recently posted videos on social media showing himself in training.
Premier League
Paper Round: United give Van Gaal £150m to spend
23/06/2015 AT 06:25
"We anticipate that Daniel will be back, hopefully to train around about September," said manager Brendan Rodgers back in May.
"Obviously it is long period of time out but we hope the problem and issues have been resolved with the operation.
"We hope he is available to train in September and then it is about getting his fitness in."
Twitter
Rodgers was asked whether, with the time it would take for Sturridge to get back to proper match fitness, the chances were they were unlikely to see the best of the striker until November.
"It is not just about fitness but football fitness, and that takes a bit of time," he added.
"The important thing will be to let him recover, work hard in his rehab and we have great support form our owners in that he is able to go to the world's leading specialists in America.
"He will work very hard to get back fit and the sooner the better for us.

Daniel Sturridge of Liverpool

Image credit: Reuters

"He has been a big miss to us this season but let's hope he can get back fit and contribute to the club.
"Once he's fully fit we know what he can produce and if he is at that level of fitness he can certainly be a key player for us."
With the likes of Mario Balotelli, Rickie Lambert and Fabio Borini set to be offloaded in the summer, Rodgers has to strengthen his forward line.
Anfield appears to be the likely destination of Burnley's out-of-contract Danny Ings but Rodgers has already spoken about the need to bring in an experienced, consistent striker.
Young Belgium international Divock Origi will return from his season-long loan spell at Lille for next season but Rodgers is not looking for him to shoulder the burden.
"Young Divock will be a great asset to us but I am more concerned about getting Daniel back as soon as possible because he is a great talent," he added.

Divock Origi Belgio - Belgium - Foto AP - Lapresse

Image credit: Eurosport

The Reds boss denied, however, he had missed out on a summer transfer target after Thursday's news PSV Eindhoven's Memphis Depay was to join Manchester United.
"It wasn't something that was ever one we were interested in," Rodgers said.
"He is a young, talented player but we already have four wingers at the club: Raheem Sterling, Jordon Ibe, Adam Lallana and Lazar Markovic.
"We have other priorities we are looking at through the course of the summer but with the players we have in those positions, particularly on the left side, we are quite well stocked."
Premier League
Video: Jimmy Carr steals the show at England midfielder Jonjo Shelvey's wedding
22/06/2015 AT 13:21
Premier League
Paper Round: United to swap De Gea for Real Madrid's Ramos
22/06/2015 AT 06:42