Gunners midfielder Mark Randall joined Burnley on loan from Arsenal in January 2008 but only started two matches for the Clarets so Wenger wants assurances that Wilshere will play regular football if he makes the short-term switch to Turf Moor.
"My response [to Coyle] is that it is possible under the condition that he plays," Wenger told arsenal.com.
"For us Jack Wilshere is in a period where he needs to play.
"Burnley is a very good club that I respect. They play good football but first of all Jack must want to do it and then we need to have a good hope that he will play if he goes somewhere on loan.
"I like the idea but at the moment I must say we are a bit short. Jack is involved with us for nearly every game."