Schefter, citing an unnamed "source close to the situation," writes the Dolphins proposed a one-year deal worth more than $2 million.
Taylor and his agent, Gary Wichard, each claimed there were no offers to consider other than the one Taylor signed Wednesday with the New York Jets.
"This is the only offer," Taylor said at a news conference Tuesday night. "There is no other offer. It's this or go join the Nationwide Tour with Jerry Rice, and I'm not very good at golf."
Wichard told Miami radio station 790 The Ticket the Dolphins "made no commitment to him. And he made a total commitment to [the Dolphins]. If there was an offer, I promise you he would have signed it last week."
In a text message to 790 The Ticket host Dan LeBatard, Taylor wrote "They offered me an extension in November for the same money as 2009. When I said I would like to negotiate in an uncapped year, they pulled the offer in December and said nothing since."