With the 2014-15 Premier League season set to get underway in just 12 days, Arsenal enters the opener against Crystal Palace with some major players having signed with the north London club. Forward Alexis Sanchez is expected to be a top contributor for the Gunners in the upcoming season, and Mathieu Debuchy and Calum Chambers have replaced Bacary Sagna and Carl Jenkinson at right back on a squad that finished just seven points from the title, won the FA Cup, and earned a spot in Champions League for the 17th consecutive year.

However, Arsene Wenger may not be done, with three high-profile names linked to the club in recent days as the deadline looms at month’s end. During the weekend, Wenger said Arsenal could sign another player with a maximum of two. While Arsenal has a well-stocked and relatively healthy squad entering the start of the season, Wenger might still have his choice of adding some star power.

Sami Khedira has just one year remaining on his contract, and Real Madrid recently added Toni Kroos from Bayern Munich, prompting widespread speculation that Khedira is likely to leave Spain for England or Germany. Arsenal and Chelsea have been rumored to be interested in Khedira, but Chelsea may have an edge considering the Blues are more likely to agree to his reported salary-wage demand of more than 150,000 pounds ($188,440) a week. However, Jose Mourinho’s midfield is already rather loaded, particularly after the addition of Cesc Fabregas. Khedira has also been linked to Bayern Munich, and Spanish publication Marca reported Bayern Munich would wait until next summer to add the 27-year-old. Daily Star reported Sunday Khedira would stay at Madrid for the upcoming season and then sign with Chelsea on a free transfer next season.

Wenger lacks a pure defensive midfielder who can play consistent minutes, so Khedira might be an ideal fit, and Arsenal might be the only club willing to bid on him this summer. The Gunners also have several other German players on the roster, including playmaker Mesut Ozil, center back Per Mertesacker and left wing Lukas Podolski, who reportedly made a push to convince Khedira to join him at the Emirates. When Wenger was asked about Khedira, the long-time Gunners boss responded: “I don’t want to give you any names. We are not close to signing anybody at the moment.”

Another notable German player has been linked to the Emirates, but his possible addition seems unlikely. Borussia Dortmund’s Mats Hummels, among the best center backs in the world and a much-publicized Manchester United target, has been linked to a move to Arsenal on a possible £30 million deal, the Daily Mirror reports. Arsenal already have a strong presence in the central defense with Mertesacker and Laurent Koscielny, while Thomas Vermaelen remains on the squad despite suggestions that he might be on the move to receive more playing time. Vermaelen has been linked to United on a 12 million-pound ($15 million) deal, according to The Guardian.

While Khedira seems like a more plausible transfer option than Hummels, Arsenal could be nearing a deal for a different defensive midfielder. According to the Evening Standard, Arsenal have bid 23.9 million pounds ($30 million) for William Carvalho. The 22-year-old Sporting Lisbon star has also been linked with Manchester United and Manchester City. Carvalho, who played for Portugal in the 2014 World Cup as one of the squad’s youngest players, has had loan spells with Fatima and Cercle Brugge after only receiving mainstay duties with Sporting in the 2013-14 season. Scouts have raved about Carvalho’s potential and his tackling abilities.

Portuguese publication O Jogo reported that Carvalho has a 37-million-pound ($46.5 million) release clause in his contract.