The 23-year-old has played for four different clubs in same number of years but wasn't able to become a regular in Chelsea's starting line-up over the past couple of seasons.
Sturridge, though, could feature alongside the in-form Luis Suarez at Old Trafford this weekend as Rodgers ponders how to set out his side against Manchester United.
Speaking ahead of the anticipated game at home against the Reds this weekend, Sir Alex wonders whether or not both strikers will start together.
"The big issue for Liverpool is whether they include new signing Daniel Sturridge," he told United Review.
"Certainly the arrival of Sturridge gives Brendan Rodgers more strength and options up front."
The 71-year old also praised the ambition of the England international as he made the switch after being denied first team chances Stamford Bridge.
"Sturridge has had a few clubs but I don't blame him for jumping at the chance of joining Liverpool because he just wasn't playing regularly with Chelsea and I always rate a player whose priority is wanting to play.
"Even so, his track record moving between a number of clubs suggests Brendan Rodgers is taking a bit of a gamble, but he clearly knows what he is doing."