The Bosnian has been in very good form ever since his move to Italy and Mourinho wants to sign the experienced striker.
Currently, Spurs do not have any quality backups for Harry Kane and the 34-year-old could play that role for Mourinho.
According to Mirror, the Tottenham manager sent scouts to watch the player in action last week.
It will be interesting to see if Spurs make their move for Dzeko in January.
The former Manchester City striker knows the Premier League well and he has done well in England in the past.