More than four hours of face-to-face discussions on Tuesday failed to resolve the differences between the Kansas City Chiefs and unsigned first-round draft choice Ryan Sims, and it appears that the former North Carolina defensive tackle will return home without a contract agreement.

In an effort to break the negotiating logjam that has kept him out of camp, Sims and agent Hadley Engelhard traveled to Kansas City on Tuesday. But late Tuesday night, Engelhard said that the two sides were still "millions of dollars apart" and that an agreement was not imminent.

"There were times I felt we were getting closer but, at the end of the day, we're sitting in a hotel room without a deal," Engelhard said. "Beyond that, I really don't know what to say."

The two sides are scheduled to speak again Wednesday morning. Engelhard and Sims, however, have a late morning flight to their respective homes and it would take significant movement to keep them in Kansas City.

"We're trying to stay optimistic but it's not easy," Engelhard said. "But they know where we're at and we'll continue to negotiate if they give us a viable reason to do so."

The sixth player selected overall, Sims is one of four first-round selections still without contract agreements, and one of two who have requested an investigation into possible collusion between the Chiefs and Vikings.

Engelhard reiterated his client had packed enough clothes to stay in Kansas City and begin work, should the two sides reach an agreement. But he also said the fact he and his client went to Kansas City to proactively attempt to settle their differences with the Chiefs should not be perceived as a sign of weakness on their part.

Until Tuesday, there had been no truly substantive discussions in recent days. Engelhard forwarded the Chiefs a new proposal on Aug. 19 but did not hear back from Kansas City officials and finally called them on Monday morning. The agent said that he "definitely made concessions" in his latest proposal. The hangup appears to be over so-called "back end" issues, principally "escalators" that would enhance the value of the contract.

In the last 12 seasons, the Chiefs have had only two first-round choices into camp on time, so the stalemate with Sims is nothing new to the franchise.

Sims, 22, appeared in 44 games and started 33 for the Tar Heels, and had 167 tackles and 14 sacks in his college career. He was elevated to the first unit in a spring minicamp but that status is obviously in jeopardy now. In fact, coach Dick Vermeil said last week that Sims would not be prepared to start the Sept. 8 opener at Cleveland.

In addition to Sims, the unsigned first-round draft choices are cornerback Quentin Jammer of San Diego (No. 5 pick overall), offensive tackle Bryant McKinnie of Minnesota (No. 7) and Arizona defensive tackle Wendell Bryant (No. 12). Sims and McKinnie have filed papers, through the NFL Players Association, suggesting the Chiefs and Vikings may have colluded in their respective negotiations.

There could be a break in Jammer negotiations, since San Diego officials flew to San Francisco on Tuesday night and were to meet with agent Mike Sullivan in the Bay Area. The two sides are in agreement on many of the primary elements of a contract, but are still approximately $1 million apart on the value of the contract in its first three seasons.

Len Pasquarelli is a senior writer for ESPN.com.