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Arsenal have been told they should have splashed out £60m in January to try and land West Ham star Jarrod Bowen.
Speaking ahead of a Carabao Cup clash between Liverpool and the Hammers last season, Klopp described Bowen as "probably my favourite player besides my players".
Foster said the suggested signing of Bowen by Arsenal would have led to mockery from the Gunners' rivals, but claimed his goal return would have compensated.
His comments came despite the 28-year-old being tied to a long-term contract at West Ham through to 2030.
"He would definitely score some goals for Arsenal," Foster said on his Fozcast podcast.
Jarrod Bowen celebrates his goal against Arsenal?
I think Jarrod Bowen would probably be open to it as well."
Foster said he believed a bid of between £50m to £60m would have been enough to twist West Ham's arm.
He is now hopeful of being picked for next month's World Cup qualifiers against Albania and Latvia at Wembley.
Bowen said: "Hopefully I'll be involved - we've spoken a couple of times, but all I can do is what I did against Arsenal, try and score goals, play my best every single week and see where it takes me.
"That's always been my mindset when it comes to the national team
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