Hiddink is in interim charge at Chelsea but his responsibilities as Russian national coach prevent him taking the job full time.
Ancelotti, who was approached about the Chelsea position in the summer before Luiz Felipe Scolari was appointed, is believed to be top of Roman Abramovich's list after the Russian FA refused to budge over Hiddink.
The Italian, however, appeared to rule himself out of the running on Saturday when he said: "I exclude the possibility of going to Chelsea."
However, Terry hopes that Hiddink's friendship with the Chelsea owner - and the Russian's political weight with his domestic football federation - can find a way of resolving the impasse.
"They have a good relationship off and on the field," Terry said.
"Things have gone very well since the manager's come in. I'm sure there will be talks ongoing. If we keep progressing well there can only be one option for that and that's for the people upstairs to make sure we get the right man. He's done brilliantly well and as I've said before he's got us together on and off the pitch.
"We'd love him to stay. He's been a breath of fresh air since he's come in and taken over. He's on us every day in training, he always wants to improve and be better and he lets no one get away with anything, whether it is on the pitch or off it. He's done fantastically well and it's down to the club to decide but at the moment we're doing very well."
While some players in the Chelsea dressing room are reported to favour a return of Jose Mourinho, Terry is adamant that even if Hiddink cannot be retained, the club should not go back to the Portuguese.
"Jose was a great manager, he's had some great times here," he said. "It's somebody else's turn now to kick on."
If that somebody else turns out to be Ancelotti, Chelsea will have to fight hard to get him. It is believed that he is still keen to stay at Milan – but only if he is able to sign some star names this summer, with Arsenal's Emmanuel Adebayor and Barcelona's Samuel Eto'o thought to be top of his list.
Milan, for their part, are tough negotiators and have strongly denied they are already looking for a replacement. "Milan has never contacted any coach with Carlo Ancelotti at the club," Milan general manager Adriano Galliani said. "Ancelotti is under contract with us through June 30, 2010."
Meanwhile Chelsea have defended raising the issue of players on yellow cards with referee Claus Bo Larsen ahead of last week's Champions League first leg defeat of Liverpool, claiming it was done at an appropriate Uefa organisational meeting.
Larsen, speaking in the Danish press, seemed to imply that Chelsea secretary David Barnard had tried to put indirect pressure on him and Uefa could launch an investigation.
Terry was among the players who were one caution away from suspension and the Chelsea captain said he was "disappointed" with how he felt certain Liverpool players, Xabi Alonso especially, got him booked in last week's 3-1 win.