That's according to a Tuesday report from James Olley of the Evening Standard, with Metro's Alex Brodie noting the money has been "promised" to the Frenchman, who said in regard to the Gunners' plans this winter after they landed Basel's Mohamed Elneny, "We are always open to exceptional cases."
Though Wenger may have those considerable funds available to him, it of course does not mean he'll be splashing it all out on one player, if indeed he brings anyone else in at all. Even £70 million might not be enough for some of the players Arsenal have been linked to, though.
For example, Brodie noted in his report that Napoli's Gonzalo Higuain is a "long-term target" for the Gunners but has a release clause of £76 million.
The Argentinian has been in exceptional form this season with 23 goals and three assists to his name in 26 appearances. Though a further £6 million isn't much of a stretch at that point, Wenger isn't likely to splash that amount of money on a 28-year-old, and Napoli aren't likely to let him go for less, as he's set to be a key figure in their title challenge in Serie A.
Likewise, Arsenal have been linked with Borussia Dortmund star Pierre-Emerick Aubameyang, but after he racked up 27 goals and six assists this campaign, the club reportedly won't even sell him for £75 million according to the MailOnline's Ben Grounds.
Per Bild (h/t Grounds), BVB chief executive Hans-Joachim Watzke said that "even if such an offer would come in, that would be irrelevant for us. We are simply not selling Auba."
Similarly, Olley's report indicated they "have asked to be kept informed of midfielder Adrien Rabiot's situation" at Paris Saint-Germain, with Brodie noting the Frenchman could cost £15 million.
However, after capturing Elneny, the Gunners seem unlikely to make further additions to their midfield this winter, even if a player of Wanyama's or Rabiot's quality could potentially be available for a reasonable price.
Amid Arsenal's shock 4-0 defeat to Southampton on Boxing Day, football writer Miguel Delaney noted the Gunners should be making a decisive move in the title race by recruiting two players in January:
Given the season in it, Arsenal should be winning this game, going top and then standing on throats by buying the two players they need...— Miguel Delaney (@MiguelDelaney) December 26, 2015
Elneny's signing has addressed one area of need in the midfield, though another forward option could be useful. A more realistic target than Higuain and Aubameyang is Athletic Bilbao's Inaki Williams, per Brodie.
The versatile 21-year-old has scored 10 goals and assisted three in an impressive season with Los Leones, and his pace and technique could see him fit in very well at the Emirates Stadium.
Arsenal blogger Andrew Allen believes the Gunners' transfer activity started and ended with Elneny:
Coquelin, Rosicky, Alexis, Welbeck on the way back. Elneny added already. You can draw a line under Arsenal's January transfer window.— Andrew Allen (@AAllenSport) January 21, 2016
Is Wenger taking a risk if he doesn't sign anyone else in January?
Indeed, Wenger has often had plenty of money available to him and rarely splashed out on big-money signings, particularly in January, so even if he does have £70 million to spend this winter it wouldn't be at all surprising if the Gunners shut up shop until the summer.
This season represents Arsenal's best chance in a decade to claim the Premier League title, so it would be risky not to make further recruitment in a bid to secure it.
If their injured players can successfully return and stay fit, it may not have been needed, but if the Gunners fall short, Wenger's failure to make serious outfield additions will be highlighted as a large factor in them missing out.