"He called the other day and told me," Marts told Swedish paper Aftonbladet.se.
"He wanted to go and put all his time in with his club. That's how he put it."
Enstrom, 28, wasn't originally named to Sweden's preliminary roster for the 2014 Winter Olympics, but was later invited to camp.
"We had a good conversation," Marts said, in reference to when he visited with Enstrom in Winnipeg in early-October. "I gave him the circumstances and told him which players he was competing with."
Marts added he was somewhat surprised by Enstrom's decision.
In 14 games with the Jets so far this season, Enstrom has registered one goal and six assists for seven points.