、、。
He's probably trying to finagle an invitation out of you.
Literal
He [topic-は], probably, inviting [manner-ように] maneuvering [copula-でしょう].
仕向ける (しむける, 'to induce, to maneuver someone into') is the key verb — he's engineering the situation so you'll invite him without him having to ask directly. ~てくれるように ('so that you'll do the favor of') sets the desired outcome. たぶん ('probably') and でしょう ('I suppose') double the hedging. The sentence describes a very Japanese social dynamic — indirect manipulation to avoid the directness of asking.