Wales believe a friendly with Ukraine would be the perfect preparation for the Euro 2016 tie with Russia.
Discussions have taken place over the prospect of arranging a match in Kiev next March.
"We're hoping that will be one of the [friendly] games," said Wales assistant manager Osian Roberts.
"It's quite obvious to see the similarities with Russia so we're trying to mirror the games in the tournament with the preparation games."
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The fixture has an obvious attraction for Ukraine too, given they will face Northern Ireland in Group C in France next summer.
Russia will be Wales' final Group B opponents in Euro 2016 on 20 June in Toulouse, following games against Slovakia (11 June) and England (16 June).
Wales' preparations for the finals began with a 3-2 loss to the Netherlands at Cardiff City Stadium in November.
There are two friendly dates designated in March, with a final warm-up match likely to be staged at the end of May, preferably at home.
Ukraine booked their place in the finals by beating Slovenia in the play-offs. They finished third in their group behind Spain and Slovakia.
"It's important that the friendly games are a useful exercise for us in preparation for the summer," added Roberts on BBC Radio Wales.
"Ukraine would be a perfect preparation game for us, no doubt about that."
Wales and Ukraine have met twice before in 2001, with both games ending 1-1 during the 2002 World Cup qualifying campaign.