Antunes, 33, is a free agent after his Getafe contract expired and is on Sporting’s list of options for the summer.
Left-back Antunes, capped 13 times by Portugal, left his homeland for Roma in 2007 and has been playing in Spain recently.
His performances in the 2018-19 season led to him being named in the La Liga Team of the Season.
And while Sporting hope to keep Man United target Mendes, 18, a huge offer could tempt them.
Antunes is the leading candidate to replace either player in the transfer window.