Beck, 19, is set to be released for loan as he seeks regular first team football.
English media sources say Famalicao are battling several League One clubs for the defender.
Born in Wrexham, joined the Reds at U13 level from Stoke City.
Beck, whose great uncle is Ian Rush, has already made two first team appearances for Liverpool, coming on as a substitute in Carabao Cups wins against Preston and Leicester as Liverpool won a domestic double.
He was also an unused substitute in three Premier League matches.
Beck scored one goal and provided three assists in Liverpool's youth team last term, also starring in the young Reds' journey to the UEFA Youth League quarter-finals, making six appearances.