Arsenal have reportedly offered the Russian club six million euros (4 million pounds) for the 24-year-old who played in last year's World Cup finals but has struggled for form this season.
"Kokorin should jump at the chance to leave Russia and go to that country," Kanchelskis, who joined United in 1991 and was a regular in two league title-winning sides, told Reuters in a telephone interview on Monday.
"The Russian championship is very weak and Alexander can progress at Arsenal."
"Arsenal are the best option for Alexander's career," Kanchelskis added. "If he is prepared to work a lot, he will not have any problems.
"He will not be like (Arsenal's former Russian forward) Andrei Arshavin and will become a top class forward for the London club."
Arsenal, tipped as favourites alongside Manchester City for the Premier League title, have only one fit specialist striker in Olivier Giroud, with England forward Danny Welbeck still out injured and Joel Campbell usually played on the flanks.
Kanchelskis was relatively unknown and inexperienced when he signed for United from Shakhtar Donetsk, but said Arsenal manager Arsene Wenger could help Kokorin improve.
"I also went to England when I was young without knowing the language," the 46-year-old Kanchelskis, who played more than 100 times for the Red Devils, said.
"I was lucky. Manchester United played in a 4-4-2 formation just like my former club Dynamo Kyiv."
"Like Dynamo Moscow, Arsenal play in a 4-2-3-1 formation, while Wenger trusts young players and is able to develop their talent," the 46-year-old added, who won the English title twice.
Dynamo are not commenting on Kokorin's potential move and according to the sports daily Sport Express the capital club want to keep hold of him and have offered him a new contract worth 2.5 million euros per year.
Kokorin, who has scored 10 goals in 36 matches for Russia, is currently on holiday in Dubai during the winter break.
Russian champions Zenit St Petersburg have also shown an interest in signing Kokorin as they only have two strikers on their books in Hulk and Artem Dzyuba.
"Kokorin is a fantastic player who Zenit would definitely want to see in their squad," Zenit's general director Maxim Mitrofanov, said.
For Zenit, it is important that Kokorin has a Russian passport as present rules state that a maximum of six 'foreign' players can appear on the pitch at any one time.
($1 = 0.9156 euros)
(Reporting By Dmitriy Rogovitskiy; editing by Martyn Herman)
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