"We have a deal worked out, that we just want to make sure the team gets signed, and everything gets done, and it gets done before the 15th (of September)," Doan said on XTRA 910 AM Radio in Arizona.
Doan, who became a free agent July 1, has maintained since then he wants to remain in Phoenix. Jamison has encountered several hurdles trying to buy the team, leaving Doan on the market.
Doan, the Coyotes captain, set a deadline of Sept. 15 for his new contract, the day the current Collective Bargaining Agreement expires.
"I will be signed by midnight on the 15th," Doan said. "I'll sign somewhere. ... My goal is to sign here."
Doan took part in an informal skate with teammates Thursday, according to AZCentral.com.
On radio, he said the other teams that expressed interest in him have been "phenomenally patient and kind and generous with some of their offers and different things." He would not name the teams that have made him an offer, but said the group he would consider, if needed, is "two or three."
"The Coyotes have been more than fair to me in their offer as well," Doan said. "Obviously to pick up your family and move would be difficult. And I've stated to anyone that has ever listened this whole time, my goal is to stay in Phoenix. And until I believe that the team is in that much trouble, then I was going to do everything I could to make it so that I had a chance to stay here."
Doan said staying put is not his only motivation. He said he was excited by the Coyotes' future with coach Dave Tippett, goalie Mike Smith, and a strong defense corps. Phoenix lost to the Los Angeles Kings in the Western Conference Finals last season.
Doan said Jamison has been told by the NHL his deal to buy the team is "all good" with the League, but the arena lease agreement with the City of Glendale (Ariz.) needs to be resolved to each sides' satisfaction.
"I want everything to be done and over with," Doan said. "I want the team to be sold, I want Mr. Jamison to be the owner, and I want us to be excited about the upcoming year.
"And that's kind of what it's been the whole time."