With no trade materializing Tuesday, Taylor remains on the physically unable to perform list, making him ineligible to play in at least the first four games of the season.
The Colts' next-best opportunity to deal Taylor could be before the NFL's Oct. 31 trade deadline.
If there's no deal by then, the Colts could use the franchise tag on Taylor and try to trade him again next offseason.
The Colts last week granted Taylor and his representatives permission to engage with other teams in an effort to find a trade partner, an atypical approach to shopping a player. The team issued a deadline of 4 p.m. Tuesday for a deal to come together, a timeline that lined up with the NFL's deadline requiring teams to trim rosters from 90 to 53 players.
It also was a deadline for the Colts to make a determination on Taylor's roster status, as he had been relegated to the active/physically unable to perform list until now. Taylor has not practiced or played in the preseason, having been sidelined since undergoing ankle surgery.
Taylor's standoff with Indianapolis harks back to the team's decision in May not to offer him a contract extension as he enters the final year of his rookie deal. Taylor led the NFL in rushing in 2021 with more than 1,800 yards before struggling with multiple setbacks with his ankle last season. After seeing teammates like Shaquille Leonard and Quenton Nelson receive extensions with a full season remaining on their rookie deals, Taylor expected he'd receive the same treatment.
But when it became apparent the team was not interested in reconsidering its stance -- and as Taylor observed the financial landscape for elite running backs like Josh Jacobs and Saquon Barkley -- he began to dig in.
General manager Chris Ballard was asked about Taylor's contract as training camp arrived. "We'll make those decisions when we need to make those decisions," he said.
Later that day, Taylor quietly requested a trade. The Miami Dolphins had been among the teams most intrigued by Taylor, but the Colts' compensation requests -- they initially were seeking a first-round pick in exchange -- proved too rich for the rest of the league.
The Colts' running-back unit in Taylor's absence consists of veterans Zack Moss and Deon Jackson and rookie Evan Hull. Moss, who is still recovering from a broken arm sustained in training camp, has never rushed for more than 481 yards in a single season. Jackson's career high, set last season, is 236 rushing yards. The Colts released veteran Kenyan Drake on Sunday among several other players at the positions.
ESPN's Stephen Holder contributed to this report.