Let Dubnyk go to UFA unless he shows he's an elite goalie this year.
Here's management 101: What is the market for the player in question? What is the supply of replacement players available?
Notable UFA goaltenders in 2014:
Henrik Lundquist
Jonas Hiller
Ryan Miller
Jaroslav Halak
Brian Elliot
Devan Dubnyk
Teams without a signed starter for 2014:
St. Louis (although they have signed J. Allen)
Anaheim (although they have Viktor Fasth for 3.4M next year)
Edmonton
Calgary (although they have K. Ramo signed for 2.9M)
New York Rangers (likely to re-sign Lundquist)
New York Islanders
Florida
Tampa Bay (who will give Bishop a chance to show he's a starter)
Buffalo
Pittsburgh (if Fleury is terrible again)
Realistically, Lundquist will stay with the NYR. If Anaheim pays Hiller market price, that's will be 5.5-6M plus 3.6M on goaltending - 9-10M on goalies - which might mean Fasth is available for trade. St. Louis may keep one of Halak or Elliot to pair with Allen moving forward.
Washington might be willing to move Holtby or Neuvirth depending on the way their season goes. Toronto might move Reimer if Bernier emerges as starter.
So, not including trade options, the Oilers will compete with the NYI, Florida, Buffalo, Tampa and Calgary for a starting goalie. I think the Oilers can easily keep Dubnyk for say 4 years at 4M per season. I don't see where the pressure is to offer that much more. I think Hiller and Miller will get the big money next summer. Halak, Dubnyk and Elliot will get second tier money unless they have break-out years. Florida and Tampa do not have reputations for spending big dollars - although the Isles might go hard for Hiller or Miller as they move to the Barclay's Center in a couple of years.
I hope Dubnyk gets the Oilers to the playoffs next season. If he does with a .915 svp and 2.50 GAA, with 40 wins, sure, lock him up for 5M per season on a 5+ year deal.
I don't think there is major pressure to do so though.
What gives the Oilers poor leverage is that Olivier Roy, Bunz, and other goalie prospects have not progressed much - we have no hope on the horizon. I do think the Oilers should be careful about term with Dubnyk if he only has an "ok" year. 3 years at 4M would be the max I would go. It's possible you can trade for an equivalent goalie (or sign a guy like Elliot) for half that amount.
Like you said Lundquist will resign with the rangers.
That leaves Hiller, Miller, Halak, Elliot, Dubnyk for St. Louis, Anahiem, Edmonton, Calgary, Islanders, Florida, Tampa, Buffalo...
5 goalies for 8 teams... Demand>>Supply which means $$$$ for the free agents
-St. Louis I would bet tries to sign one of Halak/Elliot
-Anahiem if Fasth plays well, they may let hiller walk but they'd sign a decent backup still
-Edmonton we would have to sign one of them, Hiller is the best and really i'd probably rather have dubnyk then the rest (miller hasn't been the same since his concussion)
-Calgary, I can't see Ramo being the answer so they'll need one
-Islanders, will need a goalie
-Florida, may go with Markstrom
-Tampa, depends on Bishop, but they do spend so if bishop fails they could sign one
-Buffalo, will need a goalie
So best case scenario... st. louis, edmonton, calgary, islanders, buffalo are after a goalie next year (5 goalies, 5 teams) and that's the best case.
And like was said earlier, Pittsburgh could pursue one. Also Backstrom is 35 and I could see Minnesota pursuing one, Vancouver may depending on the Loungo situation, Pavelec has been below average in Winnipeg and they may try to upgrade, Varmalov is a RFA in Colorado if he struggles they could be in the market for one as well
And last comment about trades for Reimer and Neuvirth... are they really upgrades over Dubnyk?