Willis signed for Toulouse last November after Wasps collapsed but was allowed to play for England in this year's Six Nations.
Willis left the England squad last week after a neck injury ended his World Cup.
England's performance director Conor O’Shea said he hoped the situation with Arundell would be confirmed in the next few weeks.
"They will only play for England while they are here (in camp)," he said.
"It's the best for club, it's the best for country, it's the best for the player.
Persons:
Henry Arundell, Bill Sweeney, Jack Willis, Arundell, Willis, couldn’t, England –, Sweeney, Henry, Conor O’Shea, Joe Marchant, Dave Ribbans, it's, O'Shea, Mitch Phillips, Peter Rutherford
Organizations:
England, Nations, French, Racing, London Irish, RFU, Irish, Wasps, Worcester, Samoa, Chile, Toulouse, Six Nations, Rugby Players, Association, Thomson
Locations:
MARSEILLE, France, Toulouse, England