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Jovetic, who scored his fourth Premier league goal of the season in Wednesday night's 4-1 win at Sunderland, picked up a knock early in the second-half and was replaced by James Milner after 56 minutes.
Silva, meanwhile, has not featured for City since their shock 2-0 Capital One Cup defeat to Newcastle United in October due to a knee injury, and Pellegrini revealed that the Spaniard faces a race against time to make their crucial Champions League trip Roma on Wednesday.
Captain Vincent Kompany will also be unavailable to face Everton due to a hamstring problem, but Aleksandr Kolarov and Edin Dzeko are ready to return after calf injuries.
"Kolarov and Dzeko are in the squad [to face Everton]," the Chilean told reporters at his press conference, "[but] Silva and Jovetic are out.
"We have a last test on [Kompany] on Monday to decide [if he can face Roma]. It is possible he could travel."
Youngster set for exit
The 20-year-old is currently on loan with Dutch club SC Cambuur until January 1, where he has scored three goals in 14 league appearances, with his impressive displays said to have caught the attention of Eredivise rivals AZ Alkmaar, FC Twente and FC Utrecht.
Originally arriving at the Etihad Stadium from MFK Košice in 2010, the Slovakian winger is still to make a first-team appearance for City and, with little chance of him breaking into their star-studded squad, the club are reportedly willing to let him leave for good in January.
Blues heading Down Under next summer
City have been confirmed as the second of three teams who will head to Melbourne, Australia, next July to compete in the International Champions Cup.
The club join Real Madrid as participants in the friendly tournament which will take place at the 100,000-capacity Melbourne Cricket Ground from July 18-24, with Inter Milan widely expected to be the final team.
The tournament was held in the USA this summer, with Manchester United beating Liverpool 3-1 in the final, but has now been expanded to include three teams facing off Down Under.
City themselves already have strong ties to the area, after their Abu Dhabi-based owners purchased and re-branded A-League side Melbourne Heart as Melbourne City FC earlier this year.
In a statement released to the media, chief executive Ferran Soriano said: “We are looking forward, once again, to being part of the tournament. We’re particularly excited to be visiting Melbourne, which is home to our sister club, Melbourne City.”