The Red Devils are on course to finish the runners up spot behind runaway Premier League leaders Manchester City.
Pep Guardiola’s side are 16 points ahead of their derby rivals and have scored 28 times more than Mourinho’s side.
The 20-time English champions aren’t assured a second-placed finish given Liverpool FC are two points behind the Red Devils.
Manchester United ended up sixth spot last term but won the Europa League and the League Cup under Mourinho.
The Red Devils could still win the FA Cup this term to ensure some silverware for the Portuguese head coach.
Former Manchester United defender Parker is adamant that a second-placed finish simply isn’t good enough for club.
“It’s become imperative for Manchester United to win something and finish in second,” said Parker, speaking exclusively to 888sport.
“That gap really is embarrassing and it’s just not Manchester United to settle for only finishing second. It will certainly mean a lot more to Liverpool to finish above United.
“For them that would be good. For United to finish in that way is not a good picture.”
The Red Devils were 2-0 winners against Swansea City in the Premier League at Old Trafford last weekend.
Manchester City will take on Manchester United in the Premier League on Saturday knowing that win will secure the title.
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