Warnock takes Palace to Newcastle on Saturday, but after that lengthy Premier League trip he will have little more than 48 hours to make signings before Monday's 11pm transfer deadline.
After being installed as Tony Pulis' replacement on Wednesday, Warnock wasted little time bringing Wilfried Zaha back to Selhurst Park on a season-long loan from Manchester United.
But he will have limited time on Sunday and Monday to make further additions, with Palace having been linked with Southampton defender Jack Cork and Norwich striker Gary Hooper.
"I have had 320 messages from agents and they are all brilliant players, all with different agents," said Warnock, who surprisingly came out of retirement to begin a second stint at Palace.
"I doubt we can do anything before the weekend.
"We need to get through the weekend. If we can get three or four players, I think we can hold our own.
"Hopefully by Sunday, Monday night we will have a couple of people to show you. I'm sure it will be chaos, it always is."
His first test is a tough one, although Palace head to St James' Park buoyed by a Capital One Cup win over Walsall, which saw Dwight Gayle score a hat-trick.
Warnock is keen to build on the legacy Pulis left him and admitted the chance to return to the club was just too much to resist.
"I've had four retirements but I couldn't resist," he said. "I don't think we should rest on our laurels.
"It would be easy to be disappointed when someone leaves like they have done, and it's difficult for the players because they have had such a fantastic time.
"And Tony's done a fantastic job, but now we have to regroup and look to the future and do the best we can.
"Yes, it might be difficult on Saturday when I've only been here a couple of days, but I still think we can go up there in good spirits and I'm looking forward to it."