Adebayor spent the second half of last season on loan at the Spanish giants, having become surplus to requirements at Eastlands following the arrivals of fellow strikers Mario Balotelli and Edin Dzeko.
The former Arsenal star has since returned to Manchester, only to be left out of Mancini's squad for City's pre-season tour of the USA, leading to talk of a move to Tottenham Hotspur, Marseille or back to Madrid.
The forward is currently training with the rest of City's fringe players, and his manager has insisted he won't stand in his way should Real Madrid seek to take him back to Spain.
"I hope for him that he can do this and also Real Madrid can buy him," Mancini told Sky Sports.
"If Manu is happy with this I am happy for him."
Adebayor scored eight goals in 22 appearances for Madrid, and the Togo international told Thursday's edition of Spanish sports daily AS that he was particularly keen on a return to the Bernabeu.
"I am waiting for [Real Madrid coach Jose Mourinho's] call and I hope it comes. If it was up to me I would play three or four years for Madrid and then retire in the white shirt."
Adebayor scored 19 goals in 43 matches for City since arriving from Arsenal in the summer of 2009.
