His comments come a day after UK Prime Minister Theresa May met with Russian President Vladimir Putin in side talks at the G20 summit in Hangzhou, China.
"We live in a very troubled world and there are many problems to solve, from climate change to Syria and beyond. But that said we do have to talk more than we are," McLeish said.
At their fringe meeting ahead of the economic summit, Putin and May expressed a desire to undertake greater cooperation on key issues, such as aviation security and drug trafficking. But outstanding issues remained unresolved, specifically in relation to future trade links and an end to anti-Russia sanctions.
"Nobody can be naïve about this. These would be tough discussion to get underway. There are lots of suspicions, lack of trust and doubts between all the parties but unless we talk we are not going to make progress on one front and it’s high time we started to make progress on other fronts," he said.
"We need a mature look at what we’re doing and we need to get unhooked from the many prejudices of the past which have haunted both Russia and Western Europe. This is a time for dialogue however difficult that may prove," he noted.
McLeish also gave his backing to a proposition to normalize trade with Russia that former UK Trade Minister Brian Wilson voiced in a comment to Sputnik last June.
"And by talking on trade we can maybe extend talks to other areas," McLeish added.
UK transport officials are expected to travel to Moscow soon to discuss ways in which Britain and Russia can work more closely on aviation security and Russian Foreign Minister Sergei Lavrov will meet with his British counterpart, Boris Johnson, at the next session of the UN General Assembly in New York due to open on September 13.