Manager Neil Warnock has made it clear he will give the midfielder time to mull over the new deal on offer.
"If they want to consider it for a length of time, that is all right for me. I think you have to show respect to Peter," said Warnock.
Whittingham, 32, celebrated ten years at the club last month. His current contract is due to expire this summer.
Warnock said: "He has an offer on the table. It is down to them now really. I spoke to his agent again this morning on the way in.
"I think we have to leave that down to Peter. Obviously negotiations are to and fro, but the offer is on the table and will stay on the table.
"I said to them I am not in a rush, the offer is on the table, I won't withdraw the offer."
Whittingham opened the scoring in the Bluebirds 2-0 win over Preston.
He will be looking for the chance to add to his tally against Norwich City, in Saturday's Championship clash in the Welsh capital.
Warnock has made it clear Wales international Emyr Huws and fellow midfielder Stuart O'Keefe are not in his long term plans.
Huws went on loan to Ipswich on deadline day while O'Keefe also made a loan move to League One side MK Dons.

The Bosnia-Herzegovina international is bidding for full match fitness after recovering from a hernia injury but is unlikely to start against QPR.
The visitors are without midfielder Jordan Cousins, who will miss the rest of the season with a quadricep injury.
On-loan winger Kazenga LuaLua is back in training after an ankle injury but is still a doubt for the visitors.
Bristol City head coach Lee Johnson told BBC Radio Bristol:
"We move into Friday after a good performance that was much desired against Wolves. Friday is going to be really, really important.
"If we can get a win, it really puts everybody else on the back foot, we'll claw another couple in and hopefully we'll push away as well.
"It is a massive game. I'm sure the players will give their all. We want to look ahead of us and make sure we overtake a couple of people, with Forest and Burton only a point ahead of us.
"Even QPR, six points ahead of us, if we beat them, we cut that gap to three points. That's really important. The more people we draw into it, the better."

The pedestrian was hit at the Texaco garage on Roman Farm Road, Hengrove, on Tuesday evening and trapped by the car until it stopped on Creswicke Road.
Shakrun Islam, 30, of Chipping Sodbury, is due before Bristol Crown Court on Friday. He was remanded in custody.
The victim, Kyle Clarke, died at the scene from his injuries.
His mother, Helen Stockford, said in a family statement: "We would like to thank the public and the emergency services for all their support on Tuesday night.
"We would ask the media for privacy at this time to allow us to grieve in peace."

Sakho, who is currently on loan at Crystal Palace, tested positive for the fat burner higenamine in March 2017 and served a provisional 30-day suspension.
Uefa dismissed the case in July.
European football's governing body blamed "gaps in communication" between Wada and two of its laboratories.
A Uefa report released on Thursday said it was "clearly not possible" for anyone to tell whether higenamine is a prohibited substance by reading Wada's banned list.
"The fact that the Cologne laboratory tested for higenamine but had to check with Wada before making a determination indicates a problem, as does the fact that the Lausanne laboratory does not test for it," it added.
"The onus is clearly on Wada to communicate to its laboratories what is and what is not on the prohibited list.
"There are clearly gaps in communication with regard to higenamine, something which also tends to support the suggestion that Wada's own internal procedure and analysis in respect of this substance is incomplete."
Sakho, 27, admitted taking the substance without Liverpool's knowledge but contended it was not on the banned list, which was supported by the report into the case by Uefa's control, ethics and disciplinary body.
The France international has not played for Liverpool since testing positive and moved to Palace on loan in February.
Cardiff City are waiting to discover if midfielder Peter Whittingham will sign a new contract.
[NEXT_CONCEPT]
Bristol City remain without midfielder Gary O'Neil (leg), but striker Milan Djuric is back in training.
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A man has appeared before magistrates in Bristol charged with murder after a man was knocked down and dragged under a moving car.
[NEXT_CONCEPT]
Liverpool centre-back Mamadou Sakho was suspended last season for taking a substance that was not on the World Anti-Doping Agency's (Wada) banned list, according to a Uefa report.