"I don't see any problem of Tymoshchuk coming back," Zenit's Italian coach Luciano Spalletti told the club's website on Friday.
The 34-year-old Ukraine midfielder, who captained Zenit to the Russian league title in 2007 and the UEFA Cup the following year, moved to Bayern before the 2009/10 Bundesliga season.
Asked if the addition of Tymoshchuk could create tensions in the team with Russia international Igor Denisov occupying the centre of midfield, Spalletti said: "The two have played together before, so I don't see a problem here.
"Besides, all top clubs need more than 11 [starting] players."
Zenit will also sign 22-year-old goalkeeper Yuri Ladygin from Greek side Xanthi as cover for Vyacheslav Malafeyev, Spalletti said.
However, the Italian has ruled out bringing back Arsenal forward Andrei Arshavin, whose contract with the London club expires at the end of the month.
"He hasn't played much for [Arsenal] lately. Why? You would have to ask him that question," Spalletti said in reference to the former Russia skipper, who joined Arsenal from Zenit for some 15 million pounds in January 2009.
Arshavin, who turns 32 next week, rejoined Zenit on a three-month loan from Arsenal in February last year after a turbulent year in English football but failed to rediscover his top form.
Zenit finished second behind CSKA Moscow this season after winning the league title for the past two years and qualified for the Champions League preliminary round next season.
‘The pure simplicity of the way Slot has managed the squad is probably the biggest thing I could say about him. It’s not broken, so let’s get on with it’: Liverpool legend full of admiration for Jurgen Klopp's successor at Anfield
‘I trained at Spurs and thought they’d give me a chance. But I received a letter thanking me but saying they didn’t think I was good enough – I was gutted’: How Tottenham missed out on signing Wales legend John Toshack
