Warburton was forced off after just six minutes of the game in Salford, to be replaced by Irishman Robin Copeland, and had to be taken to hospital to have the finger put back in place.
His absence clearly affected the side who threw away a 24-9 lead to lose their opening European encounter this season with Toulon coming to the Cardiff Arms Park this weekend.
However while Blues director of rugby Phil Davies initially thought he would have to cope without his star back rower, he is now optimistic that Warburton will be fit for the clash next Sunday.
Davies told the Western Mail: "He has gone to hospital to have it sorted out. Hopefully he will be back available for next weekend's game against Toulon."
The Blues will be back in action in the RaboDirect PRO12 the following week away to Leinster but have now lost their last three matches in all competitions.
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