But despite the widespread trade speculation, Taylor maintained his stance on Love's future with the Timberwolves in an interview Wednesday with NBA TV.
"My preference is that Kevin will come to [training] camp -- and I'm sure he will -- and play with the team," Taylor said.
Taylor also said that the Timberwolves would not trade Love unless they received what they perceived as "equal or more value" in the deal.
Golden State has been unwilling to include Klay Thompson in the framework of a deal. Cleveland, meanwhile, initially did not intend to part with No. 1 overall draft pick Andrew Wiggins for Love but has since changed its stance and would include him in a deal, a league source said.
"We are going to look at everything that makes sense that would make our team better," Taylor told NBA TV. "But we are not going to move a superb player like [Love] without getting equal or more value back."
Love has said he wants a change of scenery so he can win. He has not made the playoffs in each of six seasons with the Timberwolves.
"I say back to Kevin, 'Well, that's all I want, too,' " Taylor said.
ESPN.com's Marc Stein and ESPN The Magazine's Chris Broussard contributed to this report.