Sommer is set to leave Borussia Monchengladbach when his contract expires at the end of the season.
United are already looking at the possibility of adding the 33-year-old to Erik ten Hag's squad and will be able to make contact with his representatives from Jan. 1.
Ten Hag is looking to refresh the goalkeeping department ahead of next season. Martin Dubravka, signed on loan in the last summer window, is expected to return to Newcastle at the end of the campaign having made just one first team appearance at Old Trafford.
Meanwhile, Dean Henderson, who is spending the season on loan at Nottingham Forest, is due back at United in the summer after the club refused to include a buy clause in his temporary move to the City Ground.
Interest in Sommer, who was part of the Switzerland squad that reached the round of 16 at the World Cup in Qatar, will raise further doubts about David De Gea's long-term future.
De Gea has been first-choice goalkeeper under Ten Hag this season but sources have told ESPN that United are yet to open talks over a new contract.
The Spaniard's contract runs until the end of the season and the club have an option to extend it by another 12 months until the summer of 2024.
It leaves United with a decision to make over whether to allow De Gea to leave for nothing next summer or trigger an extension to protect his value.
De Gea has passed 500 appearances for United since arriving from Atletico Madrid in 2011.
He has been undisputed No. 1 at Old Trafford this season but his limitations as a ball-playing goalkeeper saw him omitted from the Spain squad by coach Luis Enrique ahead of the World Cup.