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Tottenham striker Keane has a thigh injury that sidelined him for Saturday's 2-1 pre-season friendly victory over Real Sociedad at White Hart Lane.
Manchester City captain Dunne was also absent at the weekend as his side lost 1-0 to Porto after sustaining a hamstring strain in training.
The extent of their injuries, however, means both will sit out this weekend's curtain-raising games in the Premier League.
Potentially, the duo could each be looking at a three-game absence as both have had scans on their injuries that have revealed short-term lay-offs according to Ireland manager Steve Staunton.
In Dunne's case there is even the prospect of him missing the start of Ireland's European Championship qualifying campaign as they open up with a Group D clash with Germany in Stuttgart on September 2.
Staunton today revealed: 'In Robbie's case we are possibly looking at a 10-day period, with Richard's maybe a little longer.'
That would see Spurs without Keane for Saturday's game at Bolton and next Tuesday's encounter at home to Sheffield United, as well as the prospect of Everton's visit on August 26.
As for Dunne, City look set to be without their skipper for the game against champions Chelsea on Sunday, and then the home matches with Portsmouth and Arsenal in the following seven days.