According to Law's agent, Carl Poston, Lions general manager Matt Millen was excited and surprised about how well Law worked out.
"They told us that they had to work some things around financially and they could give us an offer by Tuesday," Poston said.
The four-time Pro Bowl performer, released by the New England Patriots in February, has been rehabilitating his surgically-repaired left foot in Miami. The injury limited the 10-year veteran to just seven appearances in 2004 and he finished the season on the injured reserve list.
Law doesn't want to take a discount and wants to be paid about $6 million a year. Eight teams have shown interest in signing him, but so far the offers have been in the $1 million range or less -- although Poston and Law have said they have turned down two $6 million a year offers this offseason. Law has said he will not sign a minimum offer contract.
The session in Detroit was at least the second recent workout for Law, who had a June 22 workout in Jacksonville for Jaguars officials.
Last week, Lisa Kearns of the Miami-based SportFit Rehab and Training, the physical therapist and exercise physiologist who has been working with Law for months now, told ESPN.com that she felt the star cornerback was very close to being able to audition for any interested suitors. Kearns said she was confident Law would play in the NFL in 2005 and would perform at a high level.
"He's just about there [in his recovery]," said Kearns. "He's able to make hard cuts now and we've just got to turn that up some. But I think he looks just great."
The Lions have one Pro Bowl-caliber cornerback in Dre Bly and their other starter, Fernando Bryant is viewed as a solid defender, but one coming off a subpar season that was affected by injuries.
Detroit signed veteran free agent cornerback R.W. McQuarters two months ago, after he was released by the Chicago Bears, and invested a third-round draft choice on former Stanford corner Stanley Wilson.
Law, 31, has 36 career interceptions and 122 passes defensed in 141 games, all with New England, which selected the former University of Michigan star in the first round of the 1995 draft.
ESPN.com writers John Clayton and Len Pasquarelli contributed to this report.