Ian Collinson, 73, was last seen at 12.30pm on Tuesday, August 23 on the bridge over the A1 near Hartley Wood in Micklefield.
Now police say they are “very concerned” for the welfare of the pensioner, after specialist teams were called in to join the search.
Detective Inspector Paul Hobson, of Leeds District CID, said: “Ian is a well known in the community and a number of people have come forward with information - we are grateful to everyone who has helped and I would strongly urge anyone who has any information who hasn’t come forward already to do so.
“People can also help by sharing our appeal on social media.”
Mr Collinson, who is from Micklefield, is known to regularly travel to Garforth, South Milford and Leeds city centre by bus.
He also visits Crossgates and Sherburn-in-Elmet and goes on long walks.
Since he was reported missing, officers have deployed specialist search teams, supported by volunteers from Calder Valley Search and Rescue Team, in the hunt for Mr Collinson.
Officers from the Yorkshire and the Humber Underwater Search and Marine Unit have also been searching nearby waterways.
And checks have been made with hospitals and public transport services.
Mr Collinson is described as white, about 5ft 7in and slim, with short, white hair.
He wears glasses and uses a walking stick and was wearing blue jeans.
Anyone who sees Mr Collinson, or has information about his whereabouts, is asked to call police on 101 quoting log 1908 of August 23.