The 26-year-old, who has 13 tries to his credit in 35 Tests, is battling to be fit for the sport's global showpiece after suffering a serious ankle injury in the Premiership final defeat to Saracens in June.
Despite the injury Eddie Jones named him in the England squad for the World Cup in Japan -- their first match is against Tonga on September 22.
"I think he's going to be touch and go for involvement in the World Cup," Baxter told BBC Radio.
"But let's cross our fingers and hope that he can come through."
There was more encouraging news for Jones with prop Mako Vunipola.
The injury-prone Saracens front row forward, who was returning to action after tearing a hamstring in the European Champions Cup win over Leinster in May, had to go off 17 minutes after replacing Joe Marler in the 57-15 thrashing of Ireland last Saturday.
"Mako Vunipola has a small tear of scar tissue which will require approximately 10 days of rehabilitation," read a statement from the Rugby Football Union (RFU).
"Ben Moon will join up with the squad as a temporary replacement to train in Treviso."