The Portugal international suffered a collarbone injury in the Reds’ 3-1 Carling Cup win over Exeter City on Wednesday night and has been ruled out for a few weeks.
Meireles came on as a second-half sub as the Reds defeated Arsenal 2-0 at the Emirates last weekend, setting up the second goal for Luis Suarez, but will now miss the Bolton clash.
"We've been quite fortunate with that. A week or two will be the maximum."
With an international break coming after that, it seems likely he will be back in action for the September 10 trip to Stoke City.