Despite bolstering their attacking ranks with the captures of Christopher Nkunku, Nicolas Jackson and Deivid Washington, the Blues have been unable to escape mid-table obscurity in the Premier League.
Injuries have restricted Nkunku to just nine appearances in a Chelsea jersey, during which time he has scored two goals, while Jackson has amassed more Premier League yellow cards than goals in the top flight.
The Senegal international, who was recently away at the Africa Cup of Nations, has netted seven times in the Premier League, but with nine bookings to his name, he is just one caution away from incurring a two-match suspension.
Eighteen-year-old Washington is also yet to make his full debut for Mauricio Pochettino's side, whose top scorer in all competitions is former Manchester City playmaker Cole Palmer with 12 efforts.
With Armando Broja also being allowed to join Fulham on loan in January ahead of a possible permanent exit this summer, additional reinforcements in attack will be targeted by Stamford Bridge chiefs in the summer months.
According to TEAMtalk - via Corriere Dello Sport - Chelsea are now the latest team to have shown an interest in Zirkzee, who left Bayern Munich for Bologna on a permanent deal in the summer of 2022.
The Italian outfit paid just €8.5m (£7.3m) for the 22-year-old but stand to make a healthy profit thanks to his form in Serie A, where he has come up with nine goals and four assists in 24 matches this season.
Zirkzee has risen to prominence after a challenging debut campaign with Bologna, in which he struck just two goals in 19 Serie A matches in 2022-23, and his 6ft 4in frame also makes him an attractive prospect.
Chelsea may have to butt heads with Man United and Arsenal to land the Dutchman, though, while Juventus, AC Milan, Roma and Barcelona have also been running the rule over him in recent months.
Zirkzee's terms with Bologna run until the end of the 2025-26 season, but there is allegedly a growing feeling that the striker will seek pastures new once the campaign concludes.
In addition, Bayern apparently negotiated a buyback clause with Bologna, and the German champions could consider taking up their option if Harry Kane and Man United-linked Mathys Tel do not stick around.
As well as Zirkzee, Chelsea have supposedly learned that Kane is not completely satisfied with life at Bayern Munich and could try to tempt the ex-Tottenham Hotspur man into a sensational Premier League return this summer.
Napoli's Victor Osimhen and Brentford's Ivan Toney remain high on the Blues' shortlist too, as Partenopei and Bees chiefs have conceded that their leading marksmen will likely be sold in the upcoming window.
Chelsea are now facing incredibly stiff competition for Osimhen, though, as Paris Saint-Germain have purportedly made him their number one target to replace Real Madrid-bound Kylian Mbappe.