Elsewhere, Pep Guardiola finally landed Leicester's Riyad Mahrez for a club-record fee in an otherwise quiet window so far for City while Arsenal have signed a clutch of players but no marquee names to whet the appetite.
Premier League clubs spent a record £1.4 billion ($1.8 billion, 1.57 million euros)) on players in a summer splurge last year, according to football analysts Deloitte.
But there is nothing so far to match the arrival of Paul Pogba at Manchester United two years ago in a then world-record deal or Alexis Sanchez's move from the Emirates to Old Trafford in January.
The transfer window closes at 1600 GMT on August 9, a day before the first game of the season, which sees Manchester United take on Leicester City.
Liverpool boss Jurgen Klopp did his business early, bringing in Brazil's World Cup goalkeeper Alisson just weeks after two shocking errors by Loris Karius in the Champions League final defeat to Real Madrid.
He also picked up midfielders Fabinho from Monaco and Naby Keita from RB Leipzig and added Stoke City's Xherdan Shaqiri to an already formidable array of attacking talent that includes Mohamed Salah.
But the German manager is warning Liverpool not to get carried away with celebrating their success in the transfer market after splurging more than £170 million.
"We need to be ready for the big challenges, the big goals," he said. "We have to be this angry, aggressive, greedy team full of desire that wants to win each game.
"All the other teams have quality as well so we need to be ready for fights, not celebrating signings and stuff."
Mourinho, unable to resist an early dig at his rival, said Liverpool's transfer activity ought to increase expectations of a first top-flight title since 1990.
"With the investments you are making last season and you make now, that will probably be the record of the Premier League this season, a team that was a finalist in the Champions League -- you have to say you are a big candidate, you have to win," Mourinho said during United's pre-season tour of the United States, during which they were thumped 4-1 by Liverpool.
The United boss himself has cut an increasingly frustrated figure in the build-up to the season, lamenting his failure to land his top targets.
The Portuguese is desperate to close the gap to Guardiola's side but so far has just picked up Brazil midfielder Fred, who did not play a single minute at the World Cup in Russia, young defender Diogo Dalot from Porto, and veteran goalkeeper Lee Grant.
City, who finished 19 points clear of United last season, have been relatively quiet this time around but they finally snared Mahrez for £60 million, further enhancing their dazzling forward options.
The City boss said he was unfazed by Liverpool's lavish spending, remaining happy with the nucleus of the squad that romped to the Premier League title.
"Every club does what they believe, I understand completely," he said. "They are contenders to win the title, Liverpool are always a contender because of the history they have."
Hazard to stay?
Chelsea's Eden Hazard looked like he could be at the centre of one of the biggest transfer stories of the summer when he hinted at the World Cup he might want a fresh challenge.
His comments sparked speculation he could be off to Real Madrid to replace the departed Cristiano Ronaldo.
The European champions have also been linked with Chelsea goalkeeper Thibaut Courtois and Brazil forward Willian.
Britain's Sun newspaper reported on Wednesday that Courtois has told Chelsea he will quit the club next year on a free transfer unless they sell him this summer.
The only major signing for the 2016-17 Premier League champions is Brazil midfielder Jorginho from Napoli, with new boss Maurizio Sarri professing himself bored with the transfer market.
Arsenal, preparing for a season under a new manager for the first time for more than two decades, have signed a clutch of players including Switzerland defender Stephan Lichtsteiner but Unai Emery has not yet landed a marquee name.
Tottenham, about to move into a new stadium, are the only one of the top sides not to have signed a single player.
There is still time but the clock is ticking.