Burnley are now sixteenth in the Premier League and in the midst of a battle to avoid the drop.
Ole Gunnar Solskjaer has admitted that he is not expecting any of his current players to depart from Manchester United.
The Chinese Super Leaguetransfer window does not close until February 28th.
The Belgium worldwide, 31, arrived at Old Trafford from Everton in September 2013 and went on to make 177 appearances in five-and-a-half seasons at United, scoring 22 goals.
Fellaini lifted the FA Cup, Community Shield, League Cup and most notably the Europa League during his time at Old Trafford. However, Marouane Fellaini, Joel Pereira and Matthew Willock could still leave, as reported by the Daily Mirror.
Fellaini travelled to China on transfer deadline day after a fee between the two clubs was agreed.
Asked if Martial signing a new contract could convince goalkeeper David de Gea to do likewise, Solskjaer replied: "The club's working on a few players".
That has allowed Shandong Luneng to acquire the services of an experienced performer who departs Old Trafford after five-and-a-half years.
The former United midfielder told Paddy Power: "People are getting ahead of themselves in suggesting that Solskjaer should be made permanent manager".