Pulis has won two of his three games in charge, securing Palace's first back-to-back Premier League wins since 2004 with defeats of West Ham and Cardiff, ahead of Saturday's match at Chelsea.
Asked about a possible move for Rhodes, Pulis gave the rumours short shrift.
He said: "We'll get linked with every Tom, Dick and Harry from now until the window closes, I should imagine, but the answer is no. We couldn't afford Jordan Rhodes."
Pulis does intend to be active in January, though, as Palace chase Premier League survival.
"The business that we do will determine what sort of run we can have second half of the season," Pulis said.
"There has to be a certain change around, it's just how much and what we can do in that change around that will determine our season.
"The players have been fantastic, the attitude around the club has been brilliant, but we do need some help and we do need to improve."
Pulis was pleased Cameron Jerome and Marouane Chamakh scored against Cardiff and does have another striker chomping at the bit for Premier League action.
Glenn Murray was Palace's leading scorer in the promotion-winning campaign and is nearing a return from a knee injury suffered in May.
"It'll be like signing a new player, if we have him back," Pulis said.
Pulis has had little opportunity to assess his squad since his appointment and will have even less time in the next three weeks, with five Premier League matches before the January 4 FA Cup clash with West Brom.
Newcastle, Aston Villa, Manchester City and Norwich are four of the opponents but first up is Chelsea, whose stuttering form has led to their title credentials being questioned in some quarters.
Pulis has no doubts as to the ability of Jose Mourinho's side.
He said: "I think it's absolutely amazing that people are criticising Chelsea. They're third in the Premier League, they've just won their group in Europe and they're in the quarter-finals of the League Cup. They're having a stinker, aren't they?
"They're not doing too bad from where I'm looking. I expect them to be a lot stronger in the second half of the season."
Chelsea, who beat Steaua Bucharest on Wednesday night, have conceded six goals in the last two Premier League games, but Pulis insists Palace are major underdogs going to Stamford Bridge.
He added: "We've had 10 points out of five games, a real good run, the confidence is high, they (the players) are enjoying the football at the moment.
"(But) there's a massive gulf between what Chelsea have got and what this club have got.
"It's always difficult going away and playing the top, top sides in this league. You need them to be off form, you need to be right on top of it and you need some breaks as well."
Defender Dean Moxey is doubtful with a hamstring injury.
The full-back is one of three ever-presents for the Eagles this season but went off during the first half of the defeat of Cardiff with a grade one tear and will be assessed prior to kick-off.