Gerrard was substituted during the 3-2 win over Tottenham Hotspur in the Premier League last week with a hamstring injury and initial thoughts were the Liverpool captain could be sidelined for up to three weeks - meaning he could miss the return leg of this tie as well as crucial Premier League games against Southampton and Manchester City.
Rodgers told reporters at his pre-match press conference: "He won't have a chance for tomorrow and we just need to assess on a daily basis where Steven is at."
Some managers may take tomorrow's Europa League game as an opportunity to rest players in order to keep them fresh on the domestic front, but Rodgers told reporters he wants to make every effort to win the competition after dropping down from this season's Champions League.
He said: "We want to do everything we can to win a trophy. It's a very prestigious competition and this is a tough game with Besiktas. We want to take lead away."
Tomorrow night's game is likely to be a tough affair for the Reds against opponents who are not unfamiliar with English opposition this season.
Besiktas probably count themselves unfortunate that they didn't knock Arsenal out during the Champions League qualifiers, while taking four points off Tottenham on the way to topping their Europa League group. If Liverpool were to eliminate the Turkish outfit, however, it would represent a major threat to their chances of winning the tournament slipping out of the competition.