The Reds have been in talks with Ukrainian outfit Dnipro Dnipropetrovsk over their winger Konoplyanka and it is thought it is likely to cost Liverpool a fee of around £16million if the switch occurs.
Asked on Friday afternoon what the situation was with regard to the 24-year-old Ukraine international, Rodgers said: "There is no update yet. There is obviously an interest in the player, but there is no update.
"We'll see how it evolves. It is obviously a little complicated, but the staff that are over there have done brilliant work in terms of giving us every chance to get a player.
"So we will just have to see how that develops over the course of the day.
"It has all happened very quickly. Obviously the timeline on everything makes it tight."
Asked why Konoplyanka was what Liverpool needed, Rodgers - who has not signed a player yet in the current transfer window - said: "It is not just for now - it is for the future as well.
"We are still in the middle of building here and growing the group. So I feel we will need a number of players, but January is a very difficult market in which to do that.
"I'm very happy with the group I have.
"I think every manager would like a player or a number of players that can just freshen up the group - it always helps and gives that extra motivation sometimes for players. We'll see if we can do it.
"If it doesn't work out and we don't get anyone in, then we have shown over the course of the season that this is a team that is ready to fight all the way. But let's hope we can do something."
He added: "If we can improve the group in this window it will have been great, but if it is not to be for whatever reason, I'm more than happy with what we have got.
"We have got players coming back to fitness and that will hopefully set us up for the challenge of the remaining 15 league games, plus the FA Cup."
Rodgers indicated that if there is going to be any incoming personnel on deadline day for Liverpool, Konoplyanka is likely to be their only recruit.
The manager also dismissed talk of him trying to sign Manchester City defender Micah Richards on loan.
Liverpool, currently fourth in the Barclays Premier League, beat Merseyside rivals Everton 4-0 at Anfield on Tuesday and their next match sees them face West Brom away on Sunday.