Sundin is set to become an unrestricted free agent July 1 and the Toronto Maple Leafs gave the Habs exclusive rights to negotiate with him before the market opens.
According to The Canadian Press, Gainey, who dismissed a report that the New York Rangers have contacted Sundin, has planned a trip to Sweden but has yet to finalize it.
"I've spoken to him on the phone and I've spoken to his agent," Gainey said. "He's trying to organize his ideas about what his future looks like.
"It's a window of time to present who we are, this is what it looks like and do you want to come and play? I don't know what will happen. We're interested and we just want to tell him why we are, because we think we can be good partners."
The Canadiens are expected to present Sundin with a one-year and two-year offer this week, and sources tell TFP the Habs would prefer to ink the 16-year NHL veteran to a multi-year deal.
Citing a source, TFP's Editor-in-Chief David Pagnotta claims Sundin is interested in playing for the Canadiens but has yet to decide whether he'll retire or play next season. There is also the chance Sundin waits until July 1 and entertains the thought of playing for another squad.
Meanwhile, Gainey said the Canadiens were not in the market for San Jose defenseman Brian Campbell.
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