"might be keen" is correct and usable in written English. It is typically used to express that someone is likely to have an interest in something. For example, "She might be keen to try out the new restaurant downtown.".
Too-big-to-fail foreign banks might be keen to take over lenders in India.
While China's neighbors might be keen to curtail its maritime ambitions, they are also trying to engage with the country and retain good relations.
The new captain, Alastair Cook, might be keen on a fresh start but his team surely would close ranks and Pietersen would become a total outsider.
In an age of austerity, Osborne might be keen to get this debt off the public books as quickly as possible.
Those whose flesh is less frail might be keener.
That ruling may be revisited now that a populist chief justice has retired.Consumers might be keener to pay if only they got more in return.
And many of the firms that might be keenest to sell their cars under an AutoNation brand such as South Korea's Kia are among the weakest in terms of quality, not the sort of thing an aspiring supermarket such as AutoNation needs.In this section One-and-a-half Nelson Reliance on the wrong strategy The burning issue Can America's workforce grow old gainfully?
Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.
Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com