Webber, 27 was released by the Blades and was expected to make a move to fellow Championship side Crystal Palace, but it has emerged that he is in talks with North East outfit Middlesbrough.
Boro boss Gareth Southgate told the Evening Gazette: "We were made aware of Danny's availability as a free agent and we have held talks with him."
The striker came to Bramall Lane after successful loan spell in May 2005 from Watford - he was part of the squad which won promotion to the Premier League in 2006. During his time at the Lane he made a total of 74 (+43) appearances and scored 23 goals.