Manchester United are keen to sign at least one more player before deadline day next Thursday.
They have already spent £140million on Romelu Lukaku, Victor Lindelof and Nemanja Matic.
Mourinho has taken the pressure off executive vice-chairman Ed Woodward by claiming he won’t be too downhearted if a fourth players doesn’t come through the doors at Carrington.
And Given believes the current Premier League leaders have already done their best business in this transfer window.
“(Mourinho) said recently he would like another player, perhaps, but he’s not putting the pressure on Ed Woodward to get another player in,” Given told Sky Sports.
“They’ve done some great business already with Matic and Lukaku, the spine of the team.
“In an ideal world they would want one more player in but if it doesn’t happen he’s still in a strong position this season.”
United have won their first two games of the season 4-0 – against West Ham and Swansea – and host Leicester on Saturday (5.30pm) as Mourinho seeks to maintain their strong start to the campaign.
Lukaku himself has scored three goals in two league outings for his new club, having costa United £75m when arriving from Everton last month.
Matic was a £40m buy from Chelsea, while Benfica accepted a £30m offer for centre-back Lindelof.
Inter Milan’s Ivan Perisic, Gareth Bale of Real Madrid and Monaco star Fabinho have all been targeted this summer.