Mr Wallace extended an invitation to his Russian counterpart, Sergei Shoigu, to visit London to discuss mutual security earlier this week.
Mr Shoigu has offered to meet in Moscow instead, given the last bilateral defence talks between the countries took place in London.
A senior defence source said: “The Defence Secretary is glad that Russia has accepted the invitation to talk with his counterpart.
“Given the last defence bilateral between our two countries took place in London in 2013, Russian defence minister Sergei Shoigu has offered to meet in Moscow instead.
“The Secretary of State has been clear that he will explore all avenues to achieve stability and a resolution to the Ukraine crisis. We are in communication with the Russian government.”
It comes after Downing Street warned Russia would be “punished” if the country pushes ahead with any “destabilising action” in Ukraine.
US secretary of state Antony Blinken held talks with Russian diplomats in Switzerland on Friday in a bid to avert a conflict on Ukraine’s border, where Moscow has amassed an estimated 100,000 troops.
Number 10 said if Russian president Vladimir Putin launches an offensive, there will be a “package of sweeping measures” launched by the UK and its allies against the Kremlin.
Earlier, Foreign Secretary Liz Truss warned Mr Putin he must “desist and step back” from war in Ukraine or risk being dragged into a prolonged conflict like the Soviet invasion of Afghanistan.
Speaking at the Lowy Institute in Sydney, she said: “If there is an incursion by Russia into Ukraine, it would come at a massive cost.
“We are prepared to put very severe sanctions in place, we are also working to support Ukraine in terms of defensive capability.”
A spokesman for Boris Johnson said: “I think the Prime Minister has been clear that any destabilising action by Russia in Ukraine would be a strategic mistake and would have significant consequences.
“I’ve talked about the fact that we’re working closely with our partners, including the US, to draw up a package of sweeping measures to make sure that the Russian government is punished if it crosses the line.”