Juventus and AC Milan are interested in signing Olivier Giroud from Chelsea in the January transfer window.
The 34-year-old is on a shortlist of forwards Juventus, who trail Milan by 10 points in Serie A, want along with Napoli's Arkadiusz Milik and Fernando Llorente.
Giroud has eight goals from his last eight appearances following a frustrating start to the season, where he started one of Chelsea's opening 16 matches.
The France striker is out of contract in the summer but has been given assurances he will play regularly if he stays at Stamford Bridge.
Giroud joined Chelsea from Arsenal in the January transfer window in 2018 but almost left the club 12 months ago.
He stayed last January and helped Chelsea qualify for this season's Champions League with seven goals in 12 matches after football returned from the suspension due to the pandemic.
Giroud scored 18 goals in 34 appearances for Chelsea in 2020, more than any other player but was an unused substitute in the 3-1 defeat to Manchester City.
Meanwhile, Strasbourg centre-back Mohamed Simakan, who was offered to Chelsea last summer, is in talks with AC Milan and RB Leipzig about a €20m move.
Simakan is 20 and regarded as one of the best young defenders in France.
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Carragher: Why I won't go to town on Lampard
Jamie Carragher admits he would be tougher with his criticism if another manager was responsible for Chelsea's dip, but refused to add to the mounting pressure on Frank Lampard, instead highlighting a potential lack of experience at the top level.
Chelsea's fifth Premier League defeat of the season was confirmed inside 45 minutes of Sunday's clash with Manchester City as a three-goal lead at the break laid the foundation for a comprehensive 3-1 away victory at Stamford Bridge.
A run of just one victory in six league outings has left Chelsea seven points off leaders Liverpool having played a game more, and seen Lampard's position come under intense scrutiny after registering the lowest points-per-game average of any manager of the Roman Abramovich era.
Jamie Carragher labelled Chelsea "mentally fragile" following the manner of their defeat to City, and the Sky Sports pundits insisted Lampard should be compared to those who came before him.
He said: "Having played with Frank, we get questioned whether we would be more critical of the situation if it was a different manager. They would be right, I would be a lot more critical of the managers on that list. Not because I played with Frank Lampard but because I don't expect him to win the Premier League or the Champions League [this season].
"The other managers that came in with CVs, years of experience, having won the big trophies - Jose Mourinho, Guus Hiddink, Carlo Ancelotti, all great managers - I would be more critical of them."
Keane warns: Chelsea don't give managers time
Roy Keane believes Lampard is under 'huge pressure' this season with fellow pundit Graeme Souness warning Chelsea will not show their manager 'a lot of patience'.
Lampard's points-per-game record in the Premier League at Chelsea is now 1.67, lower than any Blues boss in the Roman Abramovich era, and both Keane and Souness feel his time to prove himself will be limited.
"I didn't realise the word 'patience' exists at Chelsea, particularly for managers," said Keane. "I don't think Frank is going to get that much time. There is huge pressure this year because of the money they have spent.
"Chelsea don't give managers time. It's in their DNA and history.
"He's new to it. He's 42 years of age. (Jurgen) Klopp came from Dortmund and won big prizes over there. He's up against all these managers - (Carlo) Ancelotti, (Jose) Mourinho, (Pep) Guardiola. These guys have got CVs behind them. He won't get the time Klopp got [at Liverpool]."