So far this summer, Taylor has brought in eight players, with the latest new arrival in Arvin Appiah making his debut in Saturday's 2-1 Championship home loss to Leicester City.
With six players currently missing due to injury, the Millers' resources are being severely stretched.
Taylor is targeting a trio of additions, in an ideal world, ahead of Saturday's home game with Norwich City, with the deadline closing at 11pm on Friday.
Some fringe players are also likely to be heading out.
Taylor said: "It's a big week for us. We can't hide away from that fact.
"I think there will be players going out, potentially on loan, potentially on permanent deals.
"We're trying to free up some funds and we're going to be as aggressive as the team played on Saturday: get on the front foot and put our best offers to people. We'll see where it takes us.
"I'd love to have three more bodies in before the Norwich game.
"Not only that, there's six (injured) players to come back into it. I think four of them will be back after the Norwich game (and be available for the first match after the international break).
"Suddenly, that bench looks a lot different.
"In ten days' time, for the first time since last season, I'll have competition for places.
"There will be more pressure in training than ever as returning players breathe down other players' necks in the battle for places. That can only improve where we're at."