The former Lyon star reportedly asked to leave the Toffees just before the transfer deadline on September 1st, in a move which was ultimately rejected by Moyes.
O'Brien played the majority of last season out of position at right-back with the Republic of Ireland international hoping to be moved into his favoured centre-back spot for the 2026/27 campaign.
However, that's not appear to be in Moyes' immediate plans, and he's not started a Premier League game so far in the current campaign.
"He’s an important member of the squad, but he’s going to have to wait his turn and wait and see when the opportunity comes up for him."
If O'Brien remains on the fringes of Moyes' first XI by the start of 2027, the situation could be revisited, with several Premier League sides keen on him as an option.