Liverpool boss Klopp fended off competition from Manchester United to sign Shaqiri from Stoke last month.
The Switzerland international has enjoyed a positive start to his Anfield career, scoring against the Red Devils in a 4-1 drubbing in pre-season.
And the Liverpool Echo claim Klopp is considering whether to play Shaqiri against West Ham.
The former Inter Milan and Bayern Munich powerhouse was signed merely to be a squad player.
With Mohamed Salah, Sadio Mane and Roberto Firmino at their disposal, Liverpool already possess one of the Premier League’s most formidable attacks.
But, despite that, the Liverpool Echo claim Shaqiri may be unleashed against the Hammers in a deeper midfield role.
The two teams will do battle next Sunday, with the Reds under pressure to get their campaign off to a flier.
Out of all the top six teams, Liverpool have arguably enjoyed the best summer.
Shaqiri’s signing has given them an added option for their attack.
And fellow new signings Alisson Becker, Fabinho and Naby Keita are all upgrades on Loris Karius, Emre Can and even club captain Jordan Henderson.
Klopp was full of praise for Shaqiri after his United goal last month, saying: “For Shaq, in the moment he signed he wanted to stay immediately at Liverpool and train with us.
“I think it was a week after he finished the World Cup, so I said: ‘No, no, no. Go.’
“He came back a few days ago and he was really excited.
“For him it was very good moment in his career, having already had a real experience at Bayern [Munich], at Stoke at Inter.
“Those were important moments in his career and now we have him and he can now play together with a few really nice football players.”
Who is Liverpool winger Xherdan Shaqiri?
Honours: Swiss Super League (2010, 2011, 2012)
Swiss Cup (2010, 2012)
Bundesliga (2013, 2014)
DFB-Pokal (2013, 2014)
Champions League (2013)
UEFA Super Cup (2013)
Fifa Club World Cup (2013)