Palace have mustered just 10 goals in their opening 15 Premier League games – the worst return in the division – to leave the club facing a lengthy battle to preserve their top-flight status.
The addition of a regular goalscorer such as Rhodes – who has plundered 37 goals in 62 league games for Blackburn – would significantly boost Palace's chances of beating the drop.
Pulis, though, insists the London club cannot afford the 23-year-old Scotland international, who cost Rovers a club-record fee of £8million when he joined from Huddersfield Town in August 2012.
The Palace manager, who took charge at Selhurst Park last month, said: "We'll get linked with every Tom, Dick and Harry from now until the window closes, I should imagine.
"We couldn't afford Jordan Rhodes."
Pulis has forged a reputation for being able to move successfully in the transfer market, having signed the likes of Ryan Shawcross from Manchester United for around £1million during his time in charge of Stoke City and then helped to nurture his talent.
The Welshman added: "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."
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