No final decision from Love on whether to accept the Wolves' latest offer will be made until Wednesday, sources told Stein.
The St. Paul Pioneer Press reported Tuesday the two sides had agreed to a four-year, $62 million extension.
The report, citing a person close to the situation, said Love was expected to sign the deal Wednesday afternoon in Dallas.
Love's options, to this point, have been accepting a four-year deal from Minnesota or declining the offer and becoming a restricted free agent in July, with Minnesota then able to match any offer sheet Love would receive in free agency. To reach unrestricted free agency, Love would have to be willing to play out the 2012-13 season on a one-year qualifying offer worth just $6 million.
Love is currently eligible for the same five-year extension worth nearly $80 million that Russell Westbrook received last week from the Oklahoma City Thunder, but the Wolves have to this point in negotiations been unwilling to make Love their "designated player" and offer him a five-year max contract, maintaining that they want to keep as much future flexibility as possible as they continue to rebuild their team.
Based on the NBA's new collective bargaining agreement, every NBA team can have one "designated player" on its books whose rookie contract has been extended for five years.
The deadline for a deal is midnight Wednesday.
Asked last week by the Minneapolis Star Tribune if he could imagine not finalizing an extension before the deadline, Love said: "It wouldn't be ideal. So it would be nice to work something out. I enjoy it here, I enjoy my teammates, I enjoy the coaching staff, I enjoy the Twin Cities, even when it's cold.
"I figure if I keep playing my game, playing hard-nosed basketball, playing the way I'm supposed to play, everything will take care of itself."
Love played through illness Monday night against Houston and totaled 39 points and 12 rebounds. He's averaging 24.9 points and 13.9 rebounds this season after last year becoming the first player since Moses Malone in 1982-83 to average 20 and 15 for an entire season.
Information from ESPN.com senior NBA writer Marc Stein was used in this report.