The veteran Brazilian, whose full name is Antonio Carlos Zago, has been a key part of Fabio Capello's side, picking up the Scudetto last season.
However, it looks increasingly unlikely that a deal to keep the 32-year-old at the club will be found.
"Zago asked me for a two-year deal worth £1.25 million a year," said Sensi.
"Obviously I cannot offer this kind of deal to a player of his age.
"I will offer a one-year contract with an option on a second, if he does not agree to this then he can leave."
One major spanner in the works appears to be agent Franco Zavaglia, who is not likely to be on Sensi's Christmas card list.
"Zago's agent, Zavaglia, is not a person I would consider well adapted to dealing with me," slammed Sensi.
"As soon as Francesco Totti left this agent we agreed a new deal within half an hour.
"Players who choose to have Zavaglia represent them are going to have problems with me."
