Arsenal succeeded in getting some big business done early this summer, when completing a transfer for Swiss midfielder Granit Xhaka for around 30 million pounds ($39.5 million). But, given Arsenal’s failure to mount a Premier League title challenge last season there will be significant disappointment among Gunners supporters should the arrival of Xhaka, and young Japanese forward Takuma Asano, be Arsenal’s last business before the transfer window shuts at the end of August.

In particular, the clamor for a top-class striker remains. Olivier Giroud arguably demonstrated at Euro 2016 just why he isn’t the man to fire Arsenal to domestic and European glory. The French front man has developed a habit of impressing against more favorable opposition in matches where the spotlight is not truly on, but lacking the killer instinct when it really matters. The same was true over the past month, when Giroud scored twice against Iceland and impressed against the Republic of Ireland but made little impression in the semifinals and final against Germany and Portugal.

Arsenal boss Arsene Wenger may now have woken up to that reality. Stories coming out of Italy, including from transfer expert Ginaluca di Marzio, claim that not only will Arsenal make a renewed attempt to sign long-standing transfer target Gonzalo Higuaín, but that Giroud could be offered to Napoli as part of the deal.

The 28-year-old Higuaín is coming off the back of his best ever season, scoring a record 36 goals in Serie A. Yet his performance at this summer’s Copa America may also raise concerns that Arsenal would be getting another striker with a tendency to missing on the big occasion. For a third successive major tournament with Argentina, Higuaín missed a big chance in the final that ultimately cost his team victory.

Arsenal has been chasing Higuaín since he left Real Madrid to join Napoli three years ago, but he is not the only striker to be linked with the club of late. Various news stories suggest that Lyon’s Alexandre Lacazette is also on Wenger’s agenda. The 25-year-old scored 27 Ligue Un goals two season ago to attract the interest of big clubs across Europe. He ended up staying and signing a new contract, but the disruption of all the speculation surrounding his future contributed to a less impressive performance last term, albeit still with 21 league goals, costing him a place in France’s Euro 2016 squad.

West Ham has already had a bid of 31 million pounds ($40.9 million) rejected for the 25-year-old this summer, with Arsenal now also thought to be in the race. Lyon president Jean-Michel Aulas, though, has stressed that from his conversations with Wenger during Euro 2016, he does not think that Arsenal will be making a bid.

“I saw Arsene during France matches and he has not told me," Aulas told L'Equipe. “I don't think it's something and it seems Alex wants to spend this season with Lyon in the new stadium. He wants to know an adventure in the Champions League could be much better than last season. I think he will stay with us and we are very happy.”

One striker it now appears Arsenal can forget about luring to the Emirates Stadium this summer is Alvaro Morata. When Real Madrid bought the Spain international back from Juventus for 30 million euros ($33.3 million) last month the expectation was that it was only so that it could then sell him on for a higher price. However, it is now believed that Madrid have had a change of heart and intend to make him a key part of Zinedine Zidane’s squad next summer.

Away from strikers, a familiar name to Arsenal fans has been linked with the club once more. Julian Draxler was close to joining the Gunners from Schalke in January 2014, but a deal never materialized and he then moved to Wolfsburg a year ago. A part of Germany’s Euro 2016 squad and a starter in its semifinal loss to France, the attacking midfielder is now reported to have been the subject of a 43 million pounds ($56.7 million) bid from the Gunners.

Given the struggles of Theo Walcott and Alex Oxlade-Chamberlain last season and the fact that Tomas Rosicky has now left the club, a new attacking midfielder, capable of playing wide, may be on Wenger’s mind. The money being discussed, though, would make the 22-year-old Arsenal’s biggest ever signing.