Although Rooney will miss Sunday's clash with Liverpool after picking up a knee injury during Christmas Day training, Law has been impressed at the way he combined with Van Persie following the Dutchman's arrival from Arsenal.
Immediately prior to Rooney getting injured, the pair hit a rich vein of form.
And Law is confident if they pick up where they left off, space will have to be found for some sort of silverware in the Old Trafford trophy cabinet in May.
"If the two of them are playing together, that has to be a problem for any defence," Law told MUTV.
"As we could see in the short time they have been together, they are scoring goals.
"When you have two players like that there is a fair chance you will win the league or the Champions League. They will definitely win something."
Van Persie took his tally to 19 with his brilliant equaliser at West Ham last weekend and is already odds-on to emulate another famous United figure, Cristiano Ronaldo, by landing the PFA Player of the Year prize in consecutive seasons.
At £24million, it was felt Sir Alex Ferguson took a gamble when he went for Van Persie in the summer.
As it turned out, the money was very well spent.
"He is a strong player who scores goals," said Law.
"That is what you need. It will show in time to come that has been a terrific buy."
Once again, Liverpool are playing only a minor role in the title scrap.
The return of Luis Suarez is sure to attract plenty of attention and a frosty reception can be expected given his failure to shake Patrice Evra's hand before the corresponding fixture last term.
They have since made their peace, and Ferguson expects Sunday's game to pass off without incident.
United's incentive - beyond beating the team many of their squad, including Ryan Giggs and Paul Scholes, still regard as the major rival - is to open a 10-point lead on Manchester City, who tackle Arsenal later in the day.
However, after the events of last season, Law would not even view that advantage as a winning one.
"It couldn't get any better than last season," he said.
"After thousands of games the league was won in injury time with virtually the last kick. You will never get that again.
"But it proves the league is never over until you know you can't lose.
"Until that day, it is fatal to say who is going to win the league."
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