Hammers boss David Moyes wants to bring in a centre-back before the transfer window slams shut, but the clock is working against the Premier League club.
They are keen on Caleta-Car, however it was recently suggested their chances of landing the Croatian are slim; Marseille want a permanent sale, while West Ham have favoured a loan.
The Hammers have now made progress though, according to Italian outlet Tutto Mercato, and are closing in on Caleta-Car.
Caleta-Car is claimed to be desperate to move to the Premier League and wants to test himself in England; Marseille are looking at replacements.
He has been repeatedly linked with Premier League sides in recent transfer windows and came close to joining Liverpool.
Caleta-Car has made over 100 appearances for Marseille since joining the club from Red Bull Salzburg in 2018.
If he does not leave Marseille this month then in the summer he will have only a year remaining on his contract in France.
