The Zimbabwe striker moved to City in a £6 million deal from Portsmouth last summer but has failed to make an impact at Eastlands after being dogged by injuries.
Benjani has scored just four times in 20 appearances and Pulis is poised if City boss Mark Hughes allows the 30-year-old to leave, reports The Daily Mirror.
Meanehile, Sir Alex Ferguson will retire as Manchester United manager at the end of next season, according to his son Darren.
Speculation about when Ferguson will end his long reign at Old Trafford has been ongoing since he changed his mind about quitting when he turned 60 seven years ago.
Now Darren Ferguson, manager of League One side Peterborough, has hinted it could be the summer of 2010 when his father finally walks away from the game.
"His health is fine and he’s building a new team," said Darren. "If they (Manchester United) win (the Premier League) this year, then they catch Liverpool in terms of titles won.
"I can see him doing it this year and next — and then that might be it for him."
Meanwhile, left-back Patrice Evra has played down United’s back-to-back defeats against Liverpool and Fulham.
The France international told the Sun: "I’ve been here for three years and this is the first time I have lost two straight matches.
"I am sure it is just a little accident." — AFP.