The transfer window has been open for three weeks and, as a result, silly season is in full swing.

From trying to round up new players to seeing others potentially head for the exit, the rumour mill has well and truly started spinning.

Here are the five biggest Arsenal transfer rumours this week.

5. Alexandre Lacazette bid rejected

France’s forward Alexandre Lacazette (R) jokes with France’s forward Kylian Mbappe ahead of the friendly football match France vs Paraguay on June 2, 2017 at the Roazhon Park stadium in Rennes. (FRANCK FIFE/AFP/Getty Images)

Arsenal reportedly had a bid rejected for Lacazette.

Lyon are thought to be asking for £44m plus add-ons, taking the 26-year-old’s total price to £60m.

Lyon president, Jean-Michael Aulas, is being his normal flaky self and blowing hot and cold over whether the Ligue 1 side are actually selling the striker or not. However, it does seem as if negotiations are under way.

4. Two bids for Thomas Lemar rejected

Monaco’s French midfielder Thomas Lemar celebrates after scoring during the UEFA Champions League group E football match AS Monaco and Tottenham Hotspur FC at the Louis II stadium in Monaco on November 22, 2016. (VALERY HACHE/AFP/Getty Images)

Arsenal allegedly had a £31m bid for Monaco winger, Lemar, rejected. They then entered another one, thought to be in the region of £35m, which was also knocked back.

It’s not looking likely that Arsenal will sign the 21-year-old as Monaco aren’t willing to allow both Lemar and Tiemoue Bakayoko to leave this summer.

Bakayoko has gone to Chelsea.

3. Alexis Sanchez to Manchester City hots up

Chile’s forward Alexis Sanchez celebrates after Chile won the 2017 Confederations Cup semi-final football match between Portugal and Chile at the Kazan Arena in Kazan on June 28, 2017. (ALEXANDER NEMENOV/AFP/Getty Images)

While it seems highly unlikely, City are allegedly confident that they’ll land Alexis this summer after Bayern Munich appear to have been priced out of the running.

It’s even being reported that Pep Guardiola is willing to offer Sergio Aguero as part of a swap deal for the Chilean.

2. Arsenal end interest in Kylian Mbappe

France’s forward Kylian Mbappe (L) and France’s forward Alexandre Lacazette (R) attend a training session in Clairefontaine-en-Yvelines on June 5, 2017 as part of the team’s preparation for the upcoming WC 2018 qualifiers against Sweden on June 9. (FRANCK FIFE/AFP/Getty Images)

Arsenal have reportedly decided to get real and realise that they’re probably not going to sign Mbappe from Monaco this summer.

There’s too much competition, he’ll cost too much money, and, besides, it looks as if he’s staying at Monaco anyway.

Instead, Arsenal are going to concentrate on Lacazette.

1. Gunners turn to Riyad Mahrez instead of Lemar

MANCHESTER, ENGLAND – MAY 13: Riyad Mahrez of Leicester City looks on during the Premier League match between Manchester City and Leicester City at Etihad Stadium on May 13, 2017 in Manchester, England. (Photo by Laurence Griffiths/Getty Images)

With Monaco rejecting two of Arsenal’s bids for Lemar, Arsenal are set to turn their attention to Mahrez, who they were after last summer.

This time, the forward is up for a move, with some outlets claiming he’ll only set the Gunners back £35m.