He has laid out particular conditions in talks with the club’s senior leadership.
Carrick’s future is increasingly uncertain after Man United’s 4-1 Champions League defeat away to Como on Wednesday.
That result has left the club with only two wins from 11 matches in all competitions since the season started.
Carrick is expected to take charge for Sunday’s Premier League home game against Bournemouth, but another lopsided defeat could bring an end to the 45-year-old’s tenure at Old Trafford.
According to La Repubblica, Conte would be open to a return to the Premier League, but he made his demands clear in discussions with senior United figures this week.
The report claims Conte wants a free hand in the transfer market so he can strengthen the squad’s depth in January and next summer.
