The man was taken ill and found at the Grange park in Leominster on Friday (2 August). He is currently in Hereford Hospital where he remains in a serious condition.
Sgt Tony Lewis said: “As he is in hospital we are unable to provide a picture at this time but the man is described as white, in his 40s, of large build, with glasses, a goatee beard, a greying moustache and brown wavy hair.
“He does not have any tattoos or scars but is understood to have been wearing the shirt (pictured) at the time he took ill in the park.
“We’re urging anyone who might know who this man is to come forward. Any information, no matter how small it may seem, could help us to identify him so please get in touch.”
Anyone with information or who may know the man is asked to call West Mercia Police on 101 quoting incident 751S of 2 August.