Arsenal’s always ambitious hopes of landing Real Madrid striker Karim Benzema were dashed on Monday, when the France international emphatically stated on social media that he would be remaining at the Bernabeu. While players have said such things before and still ended up moving, there looks little prospect of such a scenario materializing this time around. Indeed, Arsenal manager Arsene Wenger conceded that the odds were always against a deal being struck.

“Yes [it’s dead],” Wenger said after the goalless draw with Liverpool on Monday. “It has always been created every week again and again but we do not master that situation. When a player has a contract it’s the club who owns the contract who decides that. Real Madrid have come out many times to say that, like we want to master the situation with the players who are under contract with us.”

It leaves Arsenal with just a week remaining if they are to ensure that Petr Cech is not their only arrival of the summer transfer window. At this late stage, with club’s seasons underway and preparations already in place for the campaign ahead, the task of procuring players with the quality to enhance a talented Arsenal squad is not an easy one. While fans may dream of superstar signings, often, as Wenger has repeatedly stated, it is unrealistic.

Here, then, are four players who Arsenal just may be able to get before the window shuts on Sept. 1.

Alexandre Lacazette (Lyon)

Make no mistake, any deal for Lacazette must still be considered a long shot. After topping the Ligue Un scoring charts last season with 27 goals, the striker was linked with some of Europe’s top clubs, including Arsenal. But when it was announced earlier this month that the 24-year-old had signed a one-year extension to his contract, even he stated that “Now the gossiping can stop.”

Uncertainty over his future, though, has reemerged following a difficult start to the season. Lacazette has yet to score in three games this season, and was even booed off by his own club’s fans after his latest scoreless match this past weekend. Arsenal could look to capitalize on that uneasy atmosphere with a late bid, although, with Lacazette under contract until 2019, it will take a massive offer to prize him away. A move next summer, when clubs will have had a chance to evaluate his ability to back up his breakthrough season, looks far more likely.

Grzegorz Krychowiak (Sevilla)

With top-class strikers at a premium at this stage, if Arsenal do strengthen their squad it may well be in the defensive midfield position instead. On Monday, Wenger dismissed the need to bolster that area, but he would be taking a major risk by going into the season with Francis Coquelin, yet to complete a full season as a starter, as his only convincing option in the position. Krychowiak is one name that has been linked, and he would be an obvious option.

The Poland international was a key part of Sevilla’s fine season last term, which saw them retain the Europa League and finish fifth in La Liga. Strong and tenacious, he would be a big boost to Arsenal’s options, and at the age of 25 should be entering his prime. Wenger may consider a release clause of 30 million euros (£21.8 million) to be excessive for a holding midfielder, but it could prove a shrewd piece of business by the Gunners.

Lucas Silva (Real Madrid)

A deal for Lucas Silva would also appear to be eminently achievable before the end of the transfer window. Arsenal had pursued the deep-lying midfielder before he move from Cruzeiro to Real Madrid in January and there are rumors that they could be again. After failing to nail down a regular place and now seeing his opportunities further limited by the signing of Mateo Kovacic, it is thought that the Brazil international is already available for loan.

According to Spanish daily AS, Arsenal top the list of Premier League clubs keen to bring him in, although French side Marseille are currently well-placed to get a deal done. Whether he is exactly what Arsenal need, though, is debatable. More of a passer than a destroyer, he could lack the physicality and defensive instincts Arsenal need in that position.

Lars Bender (Bayer Leverkusen)

It seems every transfer window for the last three years, Lars Bender, twin brother of Borussia Dortmund’s Sven, has been linked with a transfer to the Emirates. And the current window is no different, with reports this week of an £18 million offer being readied by the Gunners. The 26-year-old has been a reliable performer in the heart of Bayer Leverkusen’s midfield, and he has also won 19 caps for Germany, at times when showing his versatility by being deployed at right-back. He will be difficult to prize away, given that he has only just been elevated to the position of club captain at the German club.