The on-off transfer saga appeared to have reached a stalemate last week when the two clubs could not agree on a price for the 22-year-old who has been playing for Real’s B team in the Spanish third division.
Babbel was reportedly unhappy over Real’s refusal to lower their €8million(£6.4m) price tag closer to Hoffenheim’s which was believed to be around half that.
But the deal looks to be back on after Babbel revealed he has tabled a higher offer for the German-born former Spain Under 21 international.
“It is a fact we are just talking about details of an agreement,” former Liverpool and Germany defender Babbel told Deutsche Presseagentur.
“We still have a certain interest in the services of the player and the player definitely wants to come over to our club as well.
“We will still not do anything stupid, though, it is all up to Madrid. We have put in our new offer.
“However, the reported figure of €6million (£4.8m) is not true and Joselu has also not yet completed a medical at our club.
“If Real Madrid feels they should accept our offer he could be on his way to our club in no time. I hope he is allowed to join us of course.”