The general consensus seems to be that Lanzini can step into this role in the short term. Let's hope so.
From the youngsters, Josh Cullen may be given a go. Let's see.
Thinking completely out of the box, longer term (after Real Madrid have bought Payet for £50 million) I'm going to throw the names of Jonjo Shelvey and Jack Wilshire into the ring. This is not as "far out" as would first seem. Both grew up as big West Ham fans, surrounded by West Ham friends and family. Both are creative midfielders and English internationals. If West Ham outdo Swansea this year, why wouldn't Jonjo fancy a move back home? He is still known to be an avid Hammer. And in Wilshire's case, if he can't get a regular central position for Arsenal where does he go next? To a team just round the corner and just a few places below in the league. My brother sat next to Jack at the Wembley play off final against Blackpool and if he is not a Hammer he is a very good impersonator of one (no matter what he tells the Arsenal fans).
Whilst we on the topic of West Ham fans, get behind Louisa Johnson on X Factor who is an avid Hammer. She's definitely going to win anyway as she's a star in the making and her big ambition is to sing at the Boleyn before the season is out.