The boyhood Everton fan believes Dalglish's 'buy British' policy has established the Anfield club as a major force once again following the acrimonious end to Rafa Benitez's spell in charge and Roy Hodgson's ill-fated reign.
Three and easy: Rooney scored a quick-fire hat-trick in United's 7-0 win over Seattle Sounders
'Liverpool will challenge (for the title) this time,' said Rooney. 'They've made some really good signings under Kenny Dalglish, British players, and I'm sure they will try harder than they've ever done, fighting to be up there.
'They will think they have a chance of winning the title. The main threat is going to be from Chelsea, Liverpool , Arsenal and Manchester City. One of them, plus us, will be fighting for the title.'
Rooney was speaking after scoring a 21-minute hat-trick in United's 7-0 win over Seattle Sounders in the early hours of yesterday.
It completed a happy return to the Pacific North West for the England striker who was despatched here in very different circumstances last November to regain fitness at Nike headquarters in Oregon away from the glare of publicity and fall-out from a contract crisis that took him to the brink of leaving Old Trafford.
Fast forward eight months and Rooney's rehabilitation would appear to be complete. Having helped United regain the title and reach the Champions League final - scoring in the defeat by Barcelona at Wembley - few would argue that his importance to the club is greater than ever.
And Sir Alex Ferguson's success in deploying the Englandstriker in a deeper role has opened up possibilities for Rooney, who has set his sights on overtaking Barcelona's Lionel Messi as the top No 10 in the world.
'That's where I like playing most,' said Rooney. 'It's where I finished last season and I was really enjoying it because I think it's a position that suits me.
Messi is a great player and rightly World Player of the Year. I think, not just for me but for every footballer, that's the target you want to try to get to. Hopefully I can do that.'
On the ball: Nani impressed again for United against the American side
Michael Owen, Mame Biram Diouf, Park Ji-sung and Gabriel Obertan also scored yesterday in front of a 67,000 crowd at Seattle's CenturyLink Field while Portugal winger Nani impressed again.
And Ferguson reassured the 24-year-old over his future at the club despite the signing of Ashley Young for ?16million.
He said: 'Nani was unlucky not to be picked for the (Champions League) final. He did really well the whole season but Antonio Valencia came back and his form was so good it was difficult to leave him out of the team. (Nani) will be challenging next season and play a lot of games.'
All set: De Gea is set to be handed his debut in Chicago on Saturday night
Ferguson will give David De Gea his debut in Chicago tomorrow but admitted the position of goalkeeper remains an 'open door', with both Anders Lindegaard and Ben Amos impressing on tour.
De Gea's ?17.8m transfer from Atletico Madrid marks him out as the obvious choice to succeed Edwin van der Sar but there are concerns in the short term over the 20-year-old Spaniard's lack of experience in the Premier League and command of English.
Ferguson said: 'David De Gea will be the main choice, but we will have to see how he settles.'
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