Tony Pulis sent scouts out to watch Shelvey in the reserves last week and is interested in bringing the midfielder to the Britannia Stadium in the summer.
Despite starting the season really well and featuring in the first 14 games of the season, Shelvey has failed to impress in recent games and has been criticised for his form.
Liverpool are thought to be willing to let Shelvey go as he doesn’t feature in the plans of boss Brendan Rodgers and he would be available at a cut-price.
Stoke are eyeing up a £7million swoop for the out of favour midfielder as a possible replacement for Charlie Adam who looks set to leave the club in the summer. Adam lost his father before Christmas and is said to be unsettled at Britannia Stadium and has requested a move at the end of the season.
Jonjo Shelvey signed for Liverpool in 2010 for £1.7million.