Jose Mourinho's side, one of those thought to be in the race to sign Hulk according to his agent, per Metro's Jamie Sanderson, are also closely monitoring a big-money move for Atletico Madrid forward Diego Costa.
Per Metro, the Russian outfit have placed a £40 million price tag on the striker's head, should any clubs look to take Zenit's second-top goalscorer.
The 27-year-old Brazilian has been tipped with a move to England, and speaking with Izvestia (h/t Metro's Jamie Sanderson), agent Shandor Varga believes that English clubs sit in pole position for his signature:
"Despite the huge transfer fee required to sign Hulk, don’t rule out that he will move to one of the top clubs in Europe this summer. English clubs still have the highest chance of signing him," Varga said.
Hulk has bagged nine goals in 15 league appearances this season, per WhoScored.com; the wanted forward sits just behind left winger Danny in the club's league scorer rankings.
However, Chelsea would be best to look elsewhere, as Mourinho looks to bolster his striking ranks.
Romelu Lukaku remains in London club's books, but he is not involved within the first-team set-up as he continues his loan spell at Everton.
Given the striker's big price and inexperience in the Premier League, Mourinho would be better to consolidate the ranks that he has, with the club's previous experience with big-money flops.
With Romelu Lukaku in fine form for Everton—and still on Chelsea's books—Mourinho could yet save owner Roman Abramovich another large transfer sum by drafting Lukaku back into the first-team fold at the Bridge.
The Belgian striker has bagged 10 goals in 20 league appearances for Roberto Martinez' side this season, per WhoScored, adding to his impressive tally of 15 goals in 20 games for West Brom last season.
NBC Sport Soccer's tweet also highlight's Lukaku's track record when playing against the Premier League's top opponents:
The striker has also received a ringing endorsement from Chelsea icon Didier Drogba, speaking ahead of Ivory Coast's match with Belgium, stating his belief that the 20-year-old is better than he was at his age, according to the Mirror's Neil McLeman:
I know I am his idol and we get on well. It is flattering to see that he identifies with me. But we have to stop comparing us. He is big too, certainly, but he is already tougher and he has qualities I don't. Of course, I have some that he will only acquire with time.
He will do big things and it has already started. His progression is better than mine. At the age of 19, he was at Chelsea. I was at Le Mans.
Lukaku's Chelsea return could be curtailed after Mourinho, speaking recently at a press conference, hinted at his disappointment that the striker would rather play elsewhere on loan than fight for his place at Stamford Bridge, per London24's Tom Moore:
One signing, max two. One to leave, two to leave because they want to play more because one of the kids feels it’s better to go and play on loan somewhere. I see a very quiet summer.
However, at such a promising stage and at a young age, Mourinho may be better off looking to draft Lukaku into a starting place in his squad, rather than flashing the cash on a player who has yet to step foot in the Premier League.
The club's current strikers—Torres, Samuel Eto'o, Andre Schurrle and Demba Ba—have only hit 20 goals between them this season, with Eden Hazard, Oscar and Frank Lampard scoring 24 from midfield, per BBC Sport.
Lukaku's 10 league strikes, plus seven-year age gap between the Belgian and Hulk, make the on-loan man a more interesting, long-term prospect.