The Faroe Islands international, who scored the first ever goal at the Ricoh Arena in August 2005, was released by Blackpool in May.
Jorgensen, who has played for AFC Bournemouth, is training with former City boss Micky Adams in a bid to win a contract at Vale Park.
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Meanwhile, Bolton have loaned Temitope Obadeyi to Swindon for a month.
City got compensation for Obadeyi of £100,000 plus a cut of any sell on fees at a tribunal three years ago. He has made three substitute appearances for Bolton and played for England at U19 and U20 level.
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West Brom have denied that they are signing former City loanee Yazid Mansouri. The Algerian, who played 14 times for City, claimed on a website that he was getting interest from The Baggies. However, West Brom have firmly denied this.