Manchester City and Arsenal have been offered Monaco’s Radamel Falcao for around £55m (€70m) and are battling to sign the Colombia international before the transfer window closes at 11pm on Monday night. A deal at that price would smash the clubs’ transfer record.

Arsenal are in the hunt for a striker after the injury suffered by Olivier Giroud, who is out until the new year with a broken tibia. Their fans implored Arsène Wenger to sign a forward during Sunday’s 1-1 draw at Leicester City in which the inexperienced Yaya Sanogo led the line without distinction.

One potential handicap for City is that they are trying to make the deal happen within the constraints of Uefa’s financial fair play system. Manuel Pellegrini wants to sign Falcao but the sense at the club is that time could run out. City are allowed a net spend of £49m and have around £24m at the moment after Jack Rodwell, Javi García and Gareth Barry departed.

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. There is interest in Richards from Sunderland but his wages may be an issue.

Negredo is the prime asset among those and he has been interesting Real Madrid, but it is Valencia who are close to securing a deal for the striker on a loan deal, with an option to buy for €25m (£20m), which would take Negredo’s wages off City’s balance sheet.

One option that may be explored by City is a loan deal for Falcao, 28, with the option of buying him in January or next summer. He has been available for loan at about £20m, covering a fee to Monaco and wages. It is thought that Txiki Begiristain, the City director of football, discussed the potential transfer with Monaco during Thursday’s Champions League draw in the principality.

Falcao’s camp have been pushing to get him to Real Madrid but have encountered unexpected resistance from the decision-makers at the Bernabéu, although they have not given up hope of concluding that transfer. Falcao deleted a tweet on Saturday that indicated he was moving to the club. He claimed his account had been hacked.

Arsenal pulled off a significant coup on deadline day a year ago by signing Mesut Özil from Madrid. They have spent £57m this summer on Alexis Sánchez, Calum Chambers and Mathieu Debuchy. Wenger, asked after the match against Leicester whether money would be an issue on the final day of the window, said: “Is the amount of money we can spend unlimited? No, because that’s not the way we manage the club. We try always to make the right decision. We have resources if we think it’s the right player.”

He said of reports in South America linking Arsenal with Falcao’s compatriot Carlos Bacca, who plays for Sevilla: “I can give you my phone and in the next 24 hours you will see that you get plenty of people offered from all over the world.”

Madrid, as well as having Negredo and Falcao as options, are understood to be in talks over taking the Manchester United striker Javier Hernández on loan. Tottenham’s Roberto Soldado is another on the Spanish club’s radar. Hernández, who is also being tracked by Juventus, is one of several players whose futures at Old Trafford are in the balance. Shinji Kagawa rejoined Borussia Dortmund on Sunday for £6.3m and Danny Welbeck and Tom Cleverley may follow him out of the club.

Tottenham are the favourites to sign Welbeck, with Arsenal’s need for a striker tempting them, too, to consider the 24-year-old. However, Welbeck may remain at United, as may Cleverley, who is wanted by Aston Villa. The midfielder’s contract expires in May and, although he earns a basic £30,000 a week, considerable add-ons make his United deallucrative. He is considering whether to stay and leave as a free agent in May, should he still be out of favour. Valencia are the front-runners should he choose to go.

United’s manager, Louis van Gaal, has not ruled out a late move for Arturo Vidal of Juventus or any further strengthening before the deadline despite high-ranking sources at United claiming there is a “very low probability” of more signings.

Daley Blind’s confirmation as a United player, assuming he passes a medical and agrees personal terms, for around £15m from Ajax will take United’s summer spend to £145.7m, with Luke Shaw, Ander Herrera, Marcos Rojo and Ángel di María having already joined. Van Gaal is already working on targets to sign in January as the manager believes the squad still requires further rebuilding.

As reported by the Guardian in June Kevin Strootman, who is recovering from a serious knee injury, is the manager’s prime target for the winter window, with the Roma midfielder keen on a move to United.

Chelsea have completed the £8.5m signing of Loïc Rémy from Queens Park Rangers on a four-year deal after triggering his release clause. “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,” the striker said.

His new club are expected to loan Marco van Ginkel to Milan to trim their Premier League squad from 18 to 17 non-homegrown players to comply with Premier League rules. The Italian club have completed the signing of Fernando Torres from Chelsea on a two-year loan.

Southampton hope to make a big-money signing in Red Bull Salzburg’s Sadio Mané. They have offered about £10m for the Senegal midfielder. They will sign defender Toby Alderweireld of Atlético Madrid on loan for the season.