Burmistrov, 21, will become a restricted free agent July 5.
Jets GM Kevin Cheveldayoff shopped the young forward this past season, but wasn't able to come to terms on a trade.
According to the Free Press, the Ottawa Senators, Buffalo Sabres and New York Islanders were among the teams interested in Burmistrov at the trade deadline.
In 194 games over the past three seasons with the Jets, Burmistrov has collected 23 goals and 58 points.
Burmistrov's agent, Mark Gandler, wouldn't say much with respect to the report, only telling the Free Press, "The only question I'm going to answer is to say that Alex is not going to sign in the KHL."
Meanwhile, the Jets have not yet started contract negotiations with defenseman Zach Bogosian, who can also become an RFA this summer.