Could
Old English cunnan ‘know’ (in Middle English ‘know how to’), related to Dutch kunnen and German können ; from an Indo-European root shared by Latin gnoscere ‘know’ and Greek gignōskein ‘know’.
wiktionary
From Middle English coude, couthe, cuthe, from Old English cūþe, past indicative and past subjunctive form of cunnan(“to be able”) (compare related cūþ, whence English couth). The 'l' was added in the early 16th century by analogy with should and would; this was probably helped by the tendency for 'l' to be lost in those words (and so not written, leading to shudd, wode, etc). [1] [2]
etymonline
could (v.)
Old English cuðe, past tense of cunnan "to be able" (see can (v.1)); ending changed 14c. to standard English -d(e). The unetymological -l- was added 15c.-16c. on model of would, should, where it is historical. Could be as a response to a suggestion, indicating it may be correct, is by 1938.
