"confirmed their interest" is a correct and usable phrase in written English.
You can use it when talking about someone or something expressing a definite and certain intention to do something. For example, "The investors confirmed their interest in the new project."
Tampa Bay and the Jets were among the teams that confirmed their interest.
Wigan have confirmed their interest in Jerry Seuseu, the New Zealand Warriors' prop, for the 2005 season.
Hamburg have confirmed their interest in Arsenal's Nicklas Bendtner but fellow Bundesliga side Borussia Dortmund have quashed speculation they are chasing the striker.
None of those alternative firms has publicly confirmed their interest and in an interview with the Wall Street Journal two weeks ago Alfa Group chairman, Mikhail Fridman, claimed there were "no serious buyers" outside his own consortium.
The Catalans have confirmed their interest in signing Todd Carney, an Australian scrum half who would shade a strong field as the most notorious recent addition to the National Rugby League's Hall of Shame.
West Ham's new co-owners, David Gold and David Sullivan, confirmed their interest in relocating the club to the 80,000-capacity Olympic Stadium soon after taking over at Upton Park in January.
But they did confirm their interest in the 19-year-old, who comes on the recommendation of Roman Abramovich's personal talent-spotter Piet de Visser.
If, as seems certain, Blackburn Rovers confirm their interest in bringing Paul Ince to Ewood Park from MK Dons to be their new manager, he will become the first black Briton to break into the top flight of domestic management.
Porto later announce they have received the required compensation, with Chelsea releasing a short statement confirming their interest in Villas-Boas and their intention to agree personal terms in the near future.
United's information is that earlier this summer a forged email, purporting to originate from Old Trafford and reputedly confirming their interest in a player, was sent to another club in an apparent attempt to trigger a rival bid and increase the price.
