The Portugal international is out of contract at the end of the 2026/27 season, but the club do retain an option to invoke a 12-month extension on his present deal, taking it through to June 2028.
United are keen to avoid that situation, as they want the 32-year-old to sign a new deal, and club officials have been locked in talks with his representatives since September.
However, The Athletic reports that Fernandes has turned down United's second proposal after previously rejecting terms over the summer.
If United cannot agree a fresh deal with their skipper, the club will almost certainly activate that 12-month clause before the end of 2026.
That move would guard the club against Fernandes possibly opening talks with a non-Premier League team over a free transfer in 2027 and gives United more time to persuade their star man to stay in Manchester.