The American sustained cruciate ligament damage in a tackle with Jonny Evans in the 1-0 defeat by Manchester United two weeks ago for which the defender received a red card.
Holden is expected to be out for around six months, meaning he will miss not only Bolton's FA Cup semi-final trip to Wembley next month and the end of this season but also the start of their next campaign.
Coyle said: "Let's hope it's sooner than that but what we have to make sure is it's the right time and we're not rushing people back in, because it would be detrimental to everything we're trying to do."
It is Holden's second serious injury blow in 12 months after he suffered a broken leg on international duty last term, recovering just in time for the World Cup finals.
Source: PA
Source: PA