The Iceland international has been handed a deadline to June 30 to make a decision on his future.
Babbel revealed: "Swansea is the only club who made an offer. Still, no other club have made one. What Swansea bid is acceptable, we would do that. It's now about Gylfi and Swansea.
"How far talks are with between Liverpool and Gylfi? I can't tell."