If the transfer is completed, the 26-year-old would become Liverpool's third signing of the summer after Naby Keita and Fabinho joined the club, and would strengthen Jurgen Klopp's options in the final third of the pitch.
His Stoke side suffered relegation to the Championship last season, but he looks likely to remain in the top flight and link up with the Merseyside club.
There has been interest in Shaqiri from a number of clubs, but Liverpool are set to win the race and will activate his release clause of around £13.75m rather than thrashing out a different fee.
Stoke, who are preparing to return to the Premier League at the first attempt, have been hoping to secure Liverpool's Wales winger Harry Wilson...
Shaqiri started all of Switzerland's games at this year's World Cup, where they lost to Sweden in the last 16, and has scored 21 goals in 74 games for his country, including a last-minute victor against Serbia in the group stage in Russian Federation.
"I'm very happy to be here". To play for us these are mandatory requirements.
'We are the flawless move for him in this moment as well I think, because he needs to push himself and challenge himself and our environment encourages that. I was always an admirer of his so I'm happy to reunite with him. We will want him to express himself but also learn and improve the areas of his game where he can still make progression.
I know the coach from Germany, when he was at Dortmund. "But the added bonus now is that he knows the Premier League and what it takes to perform in this uniquely intense environment".