"Putin, I think, is betting right now that he can make time work for him," Burns said on Thursday, as quoted by US broadcaster CBS News.
"The key is going to be on the battlefield in the next six months, it seems to us," he added.
"As every month goes by," Putin "runs a greater and greater risk of losing the territory that he's illegally seized from Ukraine so far," Burns also said.
"So this next period, I think, is going to be absolutely crucial," he predicted, as quoted on the cbsnews.com website.
Burns also said that Western intelligence showed Moscow was not interested in peace talks, despite occasional reports to the contrary, CBS News reported.
Ukrainian Defence Minister Oleksii Reznikov warned this week that Russia was mobilising hundreds of thousands of new troops and planning a major new offensive around the one-year anniversary of its invasion of Ukraine on February 24.
Friday is day 345 of Russia's invasion of Ukraine.