The Portuguese coach is currently getting used to life at Old Trafford after his appointment as the club’s new manager last summer.
The Red Devils are well off the pace in the race for the Premier League title and currently trail leaders Chelsea by 14 points as they first focus on breaking back into the top four.
However, Manchester United will take on Southampton in the League Cup final later this month and will still harbour ambitions of winning the Europa League and FA Cup under Mourinho this season.
And former Liverpool midfielder Redknapp feels that should be the target for Mourinho’s men as they bid to enjoy a successful campaign.
Writing in his column for The Daily Mail, Redknapp said: “If Manchester United finish in the top four and win a trophy this season, Jose Mourinho will view that as a successful start to life at Old Trafford.
“United are still fighting in the FA Cup, League Cup and Europa League. With Southampton’s Virgil van Dijk out, I expect United to win the League Cup, but landing all three would be a statement of intent from Mourinho.
“A treble would be the perfect platform for an assault on the Premier League next season and it is what Mourinho should be targeting.”
Manchester United take on Watford at Old Trafford in their next Premier League game on Saturday.
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