Speaking to Sky Sports after his defeat of Colin Osborne on Sunday, Nicholson said: "Me and Taylor will meet at some point and he had better bring his 'A' game, because if he doesn't I will put him to bed."
Taylor, 50, admitted he is growing tired of being targeted by other players.
"I haven't actually heard the comments but people have been telling what he's been saying," said Taylor, the 15-time world champion.
"It's silly because he's not really done anything yet. My dad used to say 'shut up and let your darts do the talking'. He's putting a lot of strain on himself.
"Every time a new player comes across, it's me. Then the next one comes across and I think 'here we go'.
"I get insulted by them, they do it day-in and day-out until we have a big blazing row and then they shut up then.
"That's what's going to happen with me and Paul very soon because I'm not putting up with it any more."
Taylor, the defending World Matchplay champion, plays Wayne Jones in the second round on Thursday evening, while Nicholson faces former world champion Raymond van Barneveld 24 hours earlier.
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