"No, that's not true," Williams said.
However, sources confirmed to ESPN that the potential trade partners were informed at some point Friday that Williams did not want to play for the Vikings, as was first reported by NFL Network.
Williams' agent, Vince Taylor, also denied the reports in a statement Saturday.
"On behalf of my client Trent Williams and with the permission of the Washington Redskins I sought trade opportunities for the Redskins to trade Trent," Taylor said. "Once I identified the potential trade partners, I wanted to respect all teams' rights and the process and allowed the Redskins to negotiate directly with the other teams.
"There has been false reporting that Trent and I objected to particular trades. I will continue to respect the Redskins' right to negotiate a trade, and hope that the negotiations quickly lead to a trade that is in the Redskins' interest, Trent's interest, and the interest of the other team."
A source told ESPN that the Vikings had been among the preferred destinations for Williams and that the teams had discussed a deal for more than a month. But they did not come close to anything until Friday morning, when Minnesota increased its offer to include a second Day 3 draft pick, sources said. The Vikings had previously offered one pick on the third day.
With six teams drafting tackles in the first round Thursday, it's uncertain what teams will want to trade for Williams. The San Francisco 49ers had expressed interest, but there was no deal imminent, and sources said plenty of work remains. The 49ers likely will wait to know whether starting left tackle Joe Staley is retiring before making a move. The 49ers also would have to create more salary-cap space. If the 49ers want to acquire Williams, they would likely have to offer picks in the 2021 draft because they only have picks in the last three rounds Saturday.
Other teams, such as the Los Angeles Rams, might have interest, but lack the cap space to pull off a deal. Both the Rams (Sean McVay) and 49ers (Kyle Shanahan) have head coaches who worked with Williams in Washington.
The Redskins have maintained they don't feel they need to trade Williams this weekend if they don't like the offers.
Friday became the latest twist in a saga that began in June when Williams first requested to be traded or released.
Williams eventually told reporters he was upset over what he termed inadequate medical treatment involving a cancerous growth on his scalp. Sources with the Redskins said at the time -- and still maintain -- that it was about Williams wanting a new contract.
At the time, Williams had two years left on his deal with no guaranteed money. He is scheduled to make $12.5 million this season.
Williams reported to Washington shortly before the trade deadline on Oct. 29. He later said he was upset the organization didn't aggressively shop him, saying any trust with then-president Bruce Allen had been broken. In the fall, Redskins sources said they became more aggressive trying to trade Williams in the weeks leading up to the deadline.
Regardless, by reporting, Williams received credit for a season played, even though the Redskins flunked his physical and eventually placed him on the reserve/non-football injury list.
There was some hope the relationship could be repaired after the season. The Redskins fired Allen and head athletic trainer Larry Hess in December.
But Williams' side also was upset that new coach Ron Rivera met with free-agent tight end Greg Olsen in early March before he had contacted Williams. Rivera and Williams had one brief face-to-face conversation. Rivera has not wanted the team to extend any player contracts, including Williams', saying he wants to get to know his players first. That philosophy also applied to veteran linebacker Ryan Kerrigan, who is also entering the final year of his contract.
The Redskins gave Taylor permission to seek a trade on March 5. That would allow him to negotiate a contract with any team wanting to trade. That led to increased talks with Minnesota, which had showed the most sustained interest.
Taylor had expressed frustration with the Redskins on March 24 because no deal had been reached.
"It's time for the organization to act in a manner that is in both Williams' and the team's best interest," Taylor said in a statement released to ESPN's Adam Schefter.
ESPN's Nick Wagoner contributed to this report.