The Lionesses midfielder was stretchered off in tears during the 1-0 victory over Denmark at the Women's World Cup on Friday.
Walsh, the world's most expensive player, could be seen mouthing 'I've done my knee' and was pictured on crutches after the game.
The initial concern was that she had ruptured her anterior cruciate ligament, which would have ruled her out of the World Cup and most of next season.
England are still waiting on the results of a scan, but talkSPORT understands there is hope the damage is not as severe as first feared.
Although there is no firm conclusion, the FA are quietly optimistic the Barcelona star can remain with the group in Australia and New Zealand.
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Manager Sarina Wiegman admitted she was concerned after the victory over Denmark, which put England on the brink of qualification for the knockout stages.
Wiegman said: "Of course I'm concerned because she couldn't walk off the pitch, but we don't know yet, so we can't take any assumptions.
"Let's just wait until we really have a diagnosis and then we can tell you."
England are among the favourites for the Women's World Cup but entered the tournament without a number of key players following injuries to Beth Mead, Fran Kirby and Leah Williamson.