Goal.com revealed recently that the 22-year-old was nearing a move to the Bundesliga club, and after a friendly with Real Betis on Sunday, the coach admitted that an improved offer had been proposed.
"If Real Madrid accepts he will be on his way. I hope we see him here soon," Babbel told reporters.
Los Blancos are believed to have included a buy-back clause in the deal that could see Joselu return to the Spanish capital next season for €7.5 million (£6m) or €8m (£6.3m) the year after.
The striker was born in Stuttgart and spent four years at school in Germany and now looks set to return after three years at Real Madrid.
Joselu could join goalkeeper Tim Wiese and Switzerland international Eren Derdiyok as the main new arrivals at the Rhein-Neckar-Arena this season.