But the Ukrainian champions are confident that the former Chelsea striker would choose to stay at his hometown team where he started his career rather than return to the Barclays Premier League.
New Birmingham owner Carson Yeung is said to be interested in the 33-year-old, partly because the one-time AC Milan star is a household name in emerging football markets such as Asia.
Back to his best: Shevchenko leads the celebrations after scoring against Inter
But Dynamo president Igor Surkis said: 'I haven't received an offer, but, for me, it's pleasant that Andriy is in demand. Shevchenko is reborn, becoming as he was before leaving for Milan (in 1999). His eye for goal and speed will return.
'As for offers? It doesn't just depend on me, but also on Andriy. In the summer he made a patriotic decision, rejecting offers from Italy, Spain and Turkey. I don't think he wants anything to change.'
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The only thing that may sway Shevchenko is the views of his wife, Kristen Pazik.
He recently admitted that a key reason for leaving Milan for Chelsea in 2006 was because an English-speaking environment would suit his American partner and their children.
However, he gave up on his disastrous spell at Stamford Bridge in August and was released from his £130,000 a week contract to take a pay cut by moving back to Kiev.
Shevchenko has indicated that Dynamo will be his final club and it is understood that they are grooming him to be the successor to Russian coach Valery Gazzaev.
However, his impressive form has caught the eye outside of Ukraine. He has scored three goals in seven league appearances and was on target in the 2-1 Champions League defeat by Jose Mourinho's Inter Milan on Wednesday night.
Mourinho, who was often accused of overlooking the striker while at Chelsea, said after the match: 'Shevchenko is very much back. Here again is the player that we could see three or four years ago. He again became a great football player.'
Meanwhile, Shevchenko has called for bans for the Ukraine supporters who caused trouble during the victory over England in Dnipropetrovsk last month.
The match, which Ukraine won 1-0, was disrupted twice by flares thrown from the stands and travelling supporters also reported trouble ahead of the game.
England boss Fabio Capello hit out following the match, while the FA complained to FIFA, and now Shevchenko has added to the chorus of condemnation.
Hot reception: Ukraine fans threw flares on to the pitch in Dnipropetrovsk
'I am respectful to all the fans,' said Shevchenko, who missed a penalty in the World Cup qualifier. 'But those kids who cause disruption should be aware that they jeopardise matches being played there both for their club and country.
'This small group want to stand out, but it is wrong for them to be associated with the club, the national team or the rest of the crowd at the stadium.
'They need to consider their attitude and our authorities should take legal action to band these fans from coming to the stadium.'
Shevchenko has been named as part of the squad to face Greece in their two-leg World Cup play-off later this month.
Liverpool striker Andriy Voronin has been left out after angering boss Alexei Mikhailichenko.
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