The England striker's 18 goals in 18 Premier League starts have helped his side to second in the table as the season approaches its finale.
The Old Trafford trip represents Liverpool's last away game against a top-six side, while Tottenham, Manchester City and leaders Chelsea have all still to come to Anfield.
But Sturridge told Sky Sports News talk of a title challenge - 24 years after the club's most recent success - is still premature.
He said: "There's a long way to go. I wouldn't say we're favourites for the Premier League - there are other teams that can win it ahead of us.
"We're going to do our best in every game to work as a team and get maximum points. We don't worry about winning the league, we worry about each game that's ahead of us.
"There are massive games coming up - we've got Manchester United away and then we play Chelsea at home, Manchester City at home and Tottenham at home.
"But let's not forget we've got another six games which will be difficult. Every game's going to be a cup final and were looking forward to the task ahead."
Sturridge and Luis Suarez have scored 42 league goals between them this season, and Sturridge said: "When we go out onto the football field we like to express ourselves and I think we both give each other opportunities.
"We've assisted each other three times this season and we like to help each other play as well as we possibly can. We get on very well off the field and it's important that as a unit - not just us two - that we work hard together."
Watch Liverpool take on Manchester united as part of our Super Sunday bill this weekend. Coverage begins at 12.30pm on Sky Sports 1