Jol confirmed the Cottagers had this week seen a bid rejected for Blues striker Jerome, which was understood to be in the region of ?3million.
Dutchman Jol has been at Fulham for less than two months but it has taken him no time at all to recognise the importance of Zamora.
The 29-year-old missed half of last season with a broken leg and the Cottagers took months to get over his absence, during which they were sucked into the Barclays Premier League drop zone.
There was a wake-up call for Jol last week when the striker suffered another break, although luckily this time it was only his hand.
Jol said: "If it would've been his foot, we would've had a problem, and that is why we made a bid for this other striker."
He added: "We made a bid we thought was realistic, and they rejected that, so that was that."
Jol admitted 24-year-old Jerome did not boast a particularly impressive goalscoring record, but said: "He's good in the air, quick, and he would be a good back-up for Bobby."
Those qualities are not enough for Fulham to up their bid, according to Jol, despite City's hierarchy being willing to consider selling for the right price.
It nevertheless seems a certainty the Cottagers will continue to hunt for an understudy for a player who was their talisman during their run to the Europa League final just over a year ago.
Zamora suffered his latest injury in last Thursday's third qualifying round first leg at RNK Split after someone stood on his hand.
He will wear a cast for the next few weeks but it will not prevent him playing and he is in line to start tomorrow's return leg against Split at Craven Cottage.
There has been speculation linking Zamora with a return to Tottenham in a swap deal with Peter Crouch but Jol dismissed it.
He added: "Bobby Zamora is probably one of the most gifted players in England as a number nine."
He also insisted Fulham had made no offer for ADO Den Haag duo Wesley Verhoek and Lex Immers and said he had no interest in signing Newcastle outcast Joey Barton.
Jol has already signed two new midfielders in Marcel Gecov and Pajtim Kasami, both of whom were officially unveiled today.
The Fulham boss said: "Marcel Gecov is a Danny Murphy type of player, who can play a little bit more advanced as well.
"He's a ginger but he's a real ginger - he's very versatile, he can play, he can tackle as well.
"Pajtim is a very talented player, gifted player."
Swiss youngster Kasami, who listed Zinedine Zidane as his hero, returned the compliment, saying: "Martin Jol is the reason I'm here."
Czech Republic Under-21 international Gecov added: "I'm looking to contribute as much as I can. I'll definitely work hard for it."
Kasami made his debut as a substitute last Thursday and both he and Gecov could be involved in the squad again tomorrow.
Fulham drew the first leg 0-0 and need to win to reach the play-off round.
They will need to play a lot better than last week, according to Jol, who said: "We were, of course, satisfied with the result, but I was not happy with the performance.
"But now we play at home. I think we've got more confidence at home and we will change a few things in our approach."
Source: Team Talk
Source: Team Talk