The Red Devils are currently at the top of the Premier League table following Sunday afternoon’s 3-1 victory over Bournemouth at Vitality Stadium thanks to goals from Juan Mata, Wayne Rooney and Zlatan Ibrahimovic.
Mourinho signed Ibrahimovic on a free transfer from Ligue 1 champions Paris Saint-Germain last month, while Eric Bailly completed a £30m transfer from La Liga side Villarreal at the start of the summer.
The new United manager has also added Borussia Dortmund midfielder Henrikh Mkhitaryan to his squad in a £30m deal before the Red Devils broke the world record to sign Paul Pogba in a £92m transfer from Serie A giants Juventus.
Surprisingly, though, Parker believes his former employers still need to sign three more players if Mourinho’s side are to challenge for a top-four finish and a return to the Champions League this season.
“They still need a centre forward and a centre-half and another midfield player,” said Parker, speaking exclusively to 888sport.
“Manchester United aren’t finished yet; they can’t be because that present squad just isn’t going to win the league and Mourinho is all about winning the league.”
Parker added: “Would you say United can even finish top four after what we saw in the Bournemouth game? I’d have to say not really. Liverpool look good and Arsenal will improve. Tottenham and Chelsea are hard to break down and will be in there.
“So United have some work to do between now and the end of August to bring in at least three players to guarantee a Champions League spot and maybe win the league.”
United will host Southampton in their next Premier League game at Old Trafford on Friday night.
Read the full 888sport interview with Paul Parker, including his thoughts on how Paul Pogba may not live up to the price-tag
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