Zenit coach Andre Villas-Boas has announced his intention to step down in May and Pellegrini, who is leaving Manchester City this year, has been strongly linked with the job in Russian media.
Zenit asked Pellegrini to become their head coach in March 2014 but the 62-year-old chose to stay in Manchester. The St Petersburg club are now reportedly ready to offer him 3.5 million euros ($3.9 million) a year to take the job.
"Pellegrini is a great coach and I am one hundred percent sure that at all levels he is a much better manager than Villas-Boas," Kanchelskis, who is coaching Solyaris Moscow in the Russian second division, told Reuters by telephone.
"I don't know how quickly the Chilean will adapt to Russia, but he can certainly take Zenit to a higher level."
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Villas-Boas has enjoyed mixed fortunes at the Petrovsky Stadium.
The only major trophy he won was the Russian league title in 2015 and Zenit -- bankrolled by energy giant Gazprom -- have yet to make it past the Champions League round of 16.
Villas-Boas, 38, was handed a six-match touchline ban after pushing an official and he has been at loggerheads with the Russian Football Union (RFU) regarding the foreigners rule in domestic games which allows a coach to play a maximum of six non-Russian passport holders at any one time.
"Villas-Boas failed at Chelsea and Tottenham, but somehow found himself in St. Petersburg," Kanchelskis said.
"The club made the wrong choice and now they will need to find a replacement. Over the last 14 years Zenit have had foreign coaches," added the former Russia international who won two English Premier League titles with Manchester United.
"Vlastimil Petrzela, Dick Advocaat, Luciano Spalletti, Villas-Boas... For Russian coaches this position is a closed shop."
With nine games left in the Russian season, Zenit are fourth in the standings, six points behind leaders CSKA Moscow. They are also through to the semi-finals of the Russian Cup.
Key players, including Brazilian forward Hulk and Belgian midfielder Axel Witsel, could leave this year to play in stronger leagues but the future is still bright for Zenit.
"The team could change, but with Pellegrini they will certainly not be weaker," former Zenit and Russia forward Alexander Panov told Reuters.
"The Chilean has done well at Manchester City and has shown what a high-class coach he is having won the English title and League Cup twice," he added.
"He has a winning mentality and he has a number of qualities that the current coach of Zenit does not have."
(Editing by Ed Osmond)
