Borussia Dortmund have announced the signing of Shinji Kagawa for £6.3 million from Manchester United on a four-year contract.

Kagawa struggled to find a place in the XI ever since arriving from Dortmund in 2012 for around £14 million.

Chelsea have signed the QPR striker Loïc Rémy on a four-year deal. Chelsea triggered a £10.5 million release clause in his contract on Saturday lunchtime and he was subsequently left out of their squad to face Sunderland.

“I feel very happy and very proud. When I heard Chelsea wanted to sign me I said ‘let’s go’ straight away because they are one of the best clubs in the world,” said Rémy. “I remember the amazing atmosphere at Stamford Bridge when I played there for Marseille and I can’t wait to play for the first time in front of my new fans.”

There were reports that Arsenal were also interested in signing the striker but decided not to pursue the deal any further.

Monaco has offered Radamel Falcao to Manchester City and Arsenal at a cost of £55 million.

Arsenal has a need at striker, particularly with Olivier Giroud out until December.

City would need to offset the acquisition of Falcao by selling one or more of their players to comply with Financial Fair Play.

City would need more than to double the money available to them and would be willing to move on Álvaro Negredo, Micah Richards, Matija Nastasic and Scott Sinclair to close the gap.

City could potentially agree upon a loan deal with the option of buying him in January or next summer.

Falcao’s camp have been pushing to get him to Real Madrid but have encountered unexpected resistance from the decision-makers at the Bernabéu.

Daley Blind has been sold to Manchester United by Ajax for €18 million.

Blind is a 24-year-old defensive midfielder.

Manchester United are determined to unload several unneeded players before the end of the transfer window with targets such as William Carvalho, Arturo Vidal, Nigel de Jong and Daley Blind in mind.

United’s status as one of the world’s best paying clubs has caused them difficulty all summer to unload players, with the Guardian having learned that salaries are far higher that previously thought.

United has already paid £59.7 million to Real Madrid for Ángel di María.

United could begin by selling Danny Welbeck, who could fetch up to £20 million.

Javier Hernández, the subject of a bidding war between Valencia and Juventus, has two years remaining on a basic salary of up to £88,000, a total of £9.15 million.

Bayern Munich have signed the Spanish midfielder Xabi Alonso from Real Madrid for a fee around £8 million.

“When Bayern are interested in you then you must not hesitate for a single second,” Alonso told Germany’s Sport 1 television. “I am looking forward to what lies ahead. I am proud at my age to have another chance to play for such a great club.”

With injuries to Bastian Schweinsteiger, Javi Martínez and Thiago Alcântara in central midfield, Alonso will be expected to slot straight into Bayern’s starting XI.

“I would have a very good feeling for the club and the coach,” said sporting director Mattias Sammer. “After the injuries of Thiago and Schweinsteiger we have been looking for someone, who could help us immediately. And Xabi Alonso could play on top level for two years.”

Tottenham has signed Federico Fazio from Sevilla to a four-year contract.

Fazio had an £8 million release clause at Sevilla.

Fazio will provide added competition at centerback, where Spurs also have Jan Vertonghen, Younès Kaboul, Eric Dier and Vlad Chiriches.

Juventus and Valencia have made offers to buy Javier Hernández from Manchester United.

Both clubs have submitted bids in the region of £12 million to £15 million for Chicharito, who currently earns about £85,000 a week at Old Trafford.

United have promoted the 18-year-old James Wilson to the first-team squad and Van Gaal is interested in trying out Adnan Januzaj up front at some point.

Bayern Munich is close to a two-year £8 million deal with Xabi Alonso.

Pep Guardiola turned his attention to Alonso after the departure of Toni Kroos and the knee-ligament injury suffered by Javi Martínez.

Carlo Ancelotti has insisted upon the importance of Alonso, but the Real Madrid boardroom has had differing optionions.

Alonso was one of four deep-lying central midfielders along with Kroos, Asier Illarramendi and Sami Khedira, while the arrival of James Rodríguez increased the number of midfielders further.

AC Milan hopes to sign Fernando Torres and Marco van Ginkel from Chelsea before the end of the summer transfer window.

Milan would like to bring Torres on a season-long loan after the transfer of Mario Balotelli to Liverpool.

Administrator Adriano Galliani said on the club’s website: “We are in the last stages of the [transfer] market and we will see if we are able to acquire an important forward.

“This is our main aim. Torres is certainly an important forward and we will see if we can sign him or another player.

“Van Ginkel? It’s possible. We have written to Chelsea and are awaiting a response. We are optimistic.”