Emery can make Ten Hag's position even more precarious if his side beat United in Sunday's Premier League clash at Villa Park.
United are languishing in 13th place in the top flight following last weekend's woeful 3-0 home defeat against Tottenham.
Ten Hag's cause was hardly helped on Thursday when United blew a two-goal lead against Porto in the Europa League and needed Harry Maguire's late goal to rescue a 3-3 draw.
Villa are riding high after a memorable 1-0 win against Bayern Munich in the Champions League on Wednesday.
But with speculation mounting that United co-owner Jim Ratcliffe could axe Ten Hag, Emery defended the Dutchman ahead of their meeting this weekend.
"I have a lot of respect for him. We have lost the last four home and away games to them and they are a winning team. They beat Manchester City to win the FA Cup," Emery told reporters on Friday.
"The club is usually a winning club. They are not getting consistent form in the Premier League but I have had to think about how I prepare for this match more than the Bayern Munich game."
Fifth-placed Villa are six points ahead of United and unbeaten in their past seven games in all competitions.
Yet Emery is adamant United, who have won just two of their six league games, still pose a formidable threat.
"Sunday is a huge match for us after Bayern Munich because we are playing the best team in the world," he said.
"United are not in the Champions League, they are in the Europa, but they are a team with quality players and coach."
Emery has a habit of playing down Villa's achievements in a bid to keep his players motivated and focused.
Having led Villa into the Champions League for the first time in 41 years and masterminded their upset of Bayern, the Spaniard is not about to change his approach.
"We are not favourites to be in the top seven of the Premier League," he said when asked what Villa can achieve this season.
"We want to be a contender and we are in the process of getting points. We will have to see where we are in February."
