This is the courting period, and the Edmonton Oilers, thanks to Connor McDavid’s franchise-altering impact, are doing just that.

Like many teams this week, the Oilers have invited players to visit their city to try to sell them on the market and team, and on Tuesday, pending unrestricted free agents Milan Lucic and Jason Demers were scheduled to be in town, sources told ESPN.com.

Milan Lucic and Jason Demers are drawing interest for different reasons. Getty Images

That's a normal part of the UFA speaking window and it doesn't mean the Oilers have a leg up. But they're certainly doing their best to sell themselves to potential UFA targets.

We told you last month about Edmonton's strong interest in Lucic, as GM Peter Chiarelli knows the hulking winger well from their days together with the Boston Bruins, and Lucic is intrigued, given the possibility of riding shotgun with No. 97 on the up-and-coming Oilers.

But Lucic will certainly consider several offers -- I'm hearing 10 teams have expressed interest -- that will be on the table come Friday because the winger is generally regarded as the No. 2 UFA, behind Steven Stamkos. Lucic was in Vancouver to visit with the Canucks on Monday.

As for Demers, he's in demand as well, with agent Bob Sauve saying Tuesday that several teams have already called about the Dallas Stars blue-liner whose contract expires Thursday at midnight.

"[Stars GM] Jim Nill told us two weeks ago that he would let Jason hit the free-agent market," Sauve said over the phone Tuesday. "He would have liked to re-sign Jason, but he said the team would have some cap issues. He said we'd keep in touch, but that the team would let him go UFA at this point.

"Since Saturday [the opening of the UFA speaking window], we’ve had contact from teams, we've got action," added Sauve. "He should be in decent demand with [Alex] Goligoski and [Keith] Yandle signing. Jason is a young, right-handed defenseman, and there's good demand for that."

Indeed, the signings of Goligoski and Yandle have certainly depleted what was already a thin blue-line crop on the UFA market, which opens at noon on Friday.

Demers, Brian Campbell and Kris Russell still offer other areas of impact for teams looking to add a top-four blue-liner.

Just how much it's going to cost teams given the thin market ... well, that's the multimillion-dollar question.

In the case of Demers, it's no surprise that he was being wooed by the Oilers because that team is obviously desperate for a talent injection on defense. And because he's just 28 years old and a right-handed shot, it's understandable why Chiarelli would be interested in him. But several other clubs share that interest.

The Oilers are also looking into the left-shooting Russell, as they should. During this hectic week, many teams are overlapping on many players who fill the same positional need. Teams may really only want one of the players, but they need to be ready to go Plan B, Plan C, Plan D, etc., and they will have to make quick decisions Friday in doing so.

Dale Weise could be headed back to Montreal -- if the price is right. Darcy Finley/NHLI/Getty Images

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