While the midfielder’s German club, Borussia Monchengladbach, value him at £35million, Arsenal are believed to have offered just £19m.
Switzerland international Xhaka, 23, has already agreed personal terms with the Gunners, but the clubs are still far apart on a fee.
The Bundesliga side's sporting director, Max Ebert, confirmed: “There is an offer. But it does not mean that we will allow Granit a transfer for that price.
Highly-rated Xhaka has already admitted he can “absolutely” see himself playing for Arsenal next season, although it seems the Gunners are playing hardball on how much they want to pay.
“Whether there are talks or not, the clubs - Gladbach and Arsenal - know that, but as of now I am still a Gladbach player. It might change in the next weeks, or it might not change.” Said Xhaka.
“There will definitely be a decision before the European Championship [which kicks off on June 10].” He added.