The former Aston Villa man was stretchered off at the London Stadium after an innocuous challenge with Hammers forward Nikola Vlasic, and was taken straight to hospital.
A club statement later that evening said: “Ashley Westwood today suffered a serious injury to his ankle.
And Jackson hopes to give Westwood a lift by beating Southampton live on television on Thursday night, with the players keen to ‘do it for Westy’.
Jackson said: "He is such a popular member of the group and that will hopefully be something else we can tap into in terms of putting a smile on his face when he turns the telly on tomorrow night.
"It reminds you what you are doing it for.
"He is such an example and a role model around the place."
Burnley will hope Westwood has a similar turnaround in terms of returning to fitness as Liverpool midfielder Harvey Elliott, who returned to full training in January after sustaining the same sort of injury back in September.