Mourinho was sacked by Chelsea in December 2015 with the then-Premier League champions languishing in 16th, just one point above the relegation places.
And Allardyce reckons United have been played by rival clubs in this window.
"Do you want him to be very happy with the players he has around him?" said Mourinho.
From his first weeks in Manchester, Mourinho insisted Sanchez's struggles would be forgotten when he hit the ground running after a full pre-season under his belt.
The midfielder, who shone as France won the World Cup in Russian Federation last month, is reported to have told his team-mates he is desperate to leave for Spain.
Pochettino decided keeping players was the priority after a third successive top-three finish.
"We have a very good squad, with very good players, and it is very hard to add players to that. I am not confident, & the market closes today, so it's time, at least for me, to stop thinking about the market because the market will be close", he said.More news: Trouble-makers? Puel laughs off Manchester United's move for Maguire
"He worked amazingly well Monday, Tuesday, Wednesday, and he's one of the players that I have to speak to see how physically and mentally he feels".
Daley Blind and Sam Johnstone, to Ajax and West Brom respectively, are so far United's only summer sales, but talk is rife about a defensive departure given their attempts to sign a centre-back.
According to Goal, the compromised has been finally reached between the two teams on the condition that Tottenham signed a replacement first to cover for the departing player.
After storming the Championship, Nuno Espirito Santo, with super agent Jorge Mendes, has been able to strengthen his squad to the point where they look good value for a top 10 finish.
That felt like a reference to Liverpool but, more importantly for United, it was also an admission that it will need a dramatic improvement this season for his own team to bridge the gap. They can still sell players, overseas only, until August 31 as no other league has adopted the earlier deadline.
"It's a massive challenge for us to try to deliver the best tools for them to get fit and then to prepare them for the whole season, not only for one, two or three games or for one month".