Police think that David Andrew Field, 46, who works in Nottingham city centre, could be in Nottingham or Sheffield.
His partner, Denise, urged him to get in touch, saying: “Dave please come home, you are so loved, together we can sort everything.”
Mr Field’s black Fiat Punto was found on Monday at the Phoenix Park Tram Park & Ride site off junction 26 of the M1 motorway at Cinderhill, Nottingham.
Detectives think Mr Field may have got the tram towards Nottingham train station but beyond this his movements are unknown.
South Yorkshire Police Temporary Superintendent Andy Male said: “We are very anxious to speak to Mr Field and ask that he calls South Yorkshire Police on 0114 2202020.
“We can talk to him in private about the reason why he feels he needs to stay away from home.”