Solskjaer knows Morrison well from his time on the coaching staff at Manchester United and has already signed several former United players since arriving at Cardiff in January.
Reports have linked the Championship club with Morrison, who is due to appear at Manchester Crown Court on August 28 after being charged with two accounts of common assault against his former girlfriend and her mother, and harassment.
The 21-year-old is training with West Ham and can still play for the club if selected.
Speaking at the press conference ahead of Cardiff's Capital One Cup tie at Coventry, Solskjaer said: "I can't speak about other clubs' players and Rav is a West Ham player.
"But we've not made any offers whatsoever."
Such a shame. Morrison was a fantastic talent, but is pissing away his career & millions of pounds, coz he is a headcase.- Synergy