Manchester United have made a bid to sign Alexis Sánchez from Arsenal as José Mourinho attempts to scupper Manchester City’s hopes of securing the Chile forward this month.

Sánchez has already agreed personal terms worth around £250,000 a week with Pep Guardiola’s side, with City having submitted a £20m offer for the 29‑year‑old this week. Arsenal have yet to respond to that but it is understood United have since entered the race with a bid in the region of £25m.

Their proposal would also lead to Sánchez earning more than offered by City, with Mourinho believed to be confident of winning the race despite the forward having played under Guardiola at Barcelona.

United have offered Arsenal the opportunity to sign Henrikh Mkhitaryan, although a stumbling block to that deal could be the Armenian international’s wages, which are believed to be around £200,000 a week.

Sánchez’s representatives have already held talks with City having agreed to join them last summer, only for the deal to collapse when Arsenal failed to sign Thomas Lemar as a replacement on deadline day. He remains a target for Arsène Wenger, although the Frenchman is also keen on signing Malcom from Bordeaux and held preliminary talks with his agent this week. The Brazilian forward is understood to have another firm proposal to leave this month, although not from United or Tottenham, who have both been linked with the 20-year-old in recent weeks.

Bordeaux are demanding a fee of €50m (£44.5m) and would prefer to retain Malcom until the end of the season. The situation is complicated by his ownership status, with the French club reported to own only 50% of his economic rights and the remainder held by a number of agents.

Meanwhile, United’s hopes of signing Ryan Sessegnon this month have been dealt a blow after Fulham’s head of football operations insisted the 17-year-old would not be leaving Craven Cottage in January. Sessegnon, who finished as joint-top scorer at the European Under-19 Championship in June with three goals, has been tracked by United’s scouts for some time and has also attracted interest from Tottenham and Real Madrid. The European champions have watched the defender on several occasions this season and are understood to be monitoring his situation, while Spurs had a bid potentially worth more than £20m with add-ons rejected in the summer.

United had been prepared to offer an initial £25m to secure him this month but Fulham’s Tony Khan, who is the son of the club’s owner Shahid Khan, said Sessegnon has agreed to remain at Craven Cottage until the end of the season.

“As it’s been the subject of a great deal of speculation, I’d like to announce that Ryan Sessegnon is staying with Fulham and will not be departing during this January transfer window,” Khan told the Telegraph. “Ryan is a very important part of the Fulham family, and we’re grateful that he’ll be with us as we fight to achieve promotion this season.”