The newly promoted Premier League club are aware the 23-year-old has a tough route into the first team at the Reds.
And they hope he may be available, as they are eyeing a £15 million transfer, per The Sun.
Wilson was impressive during a loan spell at relegated Bournemouth this term.
But it is unclear if manager Jurgen Klopp thinks he is good enough for the Reds first eleven.
Wilson struggled for game time late in the campaign at the Cherries, and may be better suited to a lower level Premier League side.