The move came on Wednesday morning - little more than an hour after West Brom boss Pepe Mel's odds had been slashed in the same market.
However, as rumours began to circulate about Moyes' future, his odds to be the next top-flight boss out were slashed from 11/1 to 5/6 following support.
Sky Bet's head of football trading Paul Wiggins: "The money on Moyes took us by surprise this morning as the focus was largely on Pepe Mel up until about 10.30am.
"But no sooner had the West Brom boss been made odds-on, the money on Moyes became relentless, and he went in from 11/1 to 5/6 in just over an hour."
After what has been a miserable start to life at Old Trafford, the heat intensified on Moyes following Tuesday night's 2-0 Champions League defeat to Olympiacos.
It leaves United facing an uphill battle to reach the quarter-finals - the second leg takes place at Old Trafford in three weeks' time. They are 7/4 to make it through.
The reigning Premier League champions are also struggling domestically and sit just sixth in the table, 15 points behind leaders Chelsea and 11 behind fourth-placed Liverpool with a return to the Champions League looking highly unlikely.