Lambert is under mounting pressure after a home defeat to Harry Souttar and Glenn Whelan’s Fleetwood Town last night made it just four points he has picked up out of a possible 24.
Fans have started to lose patience and owner Marcus Evans has also faced criticism at Portman Road.
The Mirror claim: “Evans is now close to pulling the trigger in a bid to get a response ahead of a run of four of their next five matches at home.
“Warnock left Championship Cardiff in November after three years at the Bluebirds, including a shock promotion to the Premier League. He recently appeared on Sky Sports News’ Soccer Saturday, and was thought to have retired from management, but he could be tempted back by an offer from Ipswich.”
Lambert, who was in charge of Stoke for half-a-season in 2018, could not prevent Ipswich from suffering relegation from the Championship last term – but he was League One manager of the month in August after starting 2019/20 with four wins and two draws.
Although form dipped from November, he was handed a new five-and-a-half-year contract on January 1 – the day his side extended a winless run to eight games.
There were three wins in four in January to restore hope but the following eight matches have seen Ipswich lose six, draw one and fall to ninth.
Fleetwood boss Joey Barton says he had learnt lessons from a home defeat to Ipswich back in October.
He said: “When we played Ipswich earlier on in the season up at our place they were on a really good run (seven wins in eight games) which is really hard to do in this division.
“Then we’ve come back down here with six wins in seven games, unbeaten in 10 and one defeat in 16. You can imagine, when you’ve got my players’ mindset at the minute, there’s no fear.
“I got asked questions in the build-up to (the first meeting) and, maybe a little naively at the start of my managerial career, I thought it would be interesting to test the boundaries of Ipswich’s psychology.
“On the day it back-fired because they beat us 1-0 so I thought I’d best not try that again because it didn’t work for us last time.
“I wanted to let the players do the talking and not give Paul (Lambert) and his players any extra-motivation. They already had enough, which was having to beat us to go above us and try to maintain a promotion push.
“That’s something I’ve had to learn as part of my naivety but it’s been a steep learning curve in the job.”
He added: “You’re always trying to seek a psychological advantage and we’ve seen the likes of (Jose) Mourinho and Sir Alex Ferguson be masters of it over the years. I tried it and ultimately I ended up with a bit of egg on my face because the Ipswich players took it in the right manner and clearly responded in the right manner.
“They left a number of the articles pinned to our away dressing room. They told me in no uncertain terms about the state of those comments and for me it’s one of those, it’s a game of football where both teams are competing hard. Managers and players are also looking for little psychological edges if you can get it.
“On that occasion I tried it and lost but on this occasion I tried nothing and won, so maybe that’s the recipe for going forward.”