Carrow Road boss Chris Hughton is set to hold talks with Canaries chief executive David McNally over how to address his side's lack of goals in the January transfer window and he has identified a number of options.
Chamakh would be the most expensive because he is on a huge contract at Arsenal, who he joined on a free transfer from Bordeaux two years ago.
The Moroccan international could also be off to the African Nations Cup in the New Year, although he has not played for his country since the last tournament and is not guaranteed to be selected.
Chamakh hit a couple of goals in Arsenal's 7-5 extra-time win over Reading earlier this month and could be a good loan acquisition if he rediscovers his scoring touch after a couple of lean years in north London.
Cole looks like a risky option given his injury record but he would come with a Premier League goal pedigree, having scored 31 top flight goals in 104 starts for West Ham.
The 28-year-old is out of contract at the end of the season and his revelation last season that he took a 50 per cent pay cut when West Ham were relegated would also be of interest to the City board.
Beric, 23, is the target with the most potential - although he remains unproven at Premier League level. The Slovenian international scored for Maribor against Tottenham last week and has also been linked to Spurs and Aston Villa.