All the latest transfer news involving West Ham United...
That doesn't, however, mean the Colombian is Stratford bound, with Napoli and Champions League football his apparent preference.
The former France Under-21 international scored 17 goals to help Toulouse avoid the drop last season and, as such, has been linked with a host of clubs across the continent.
The target man played under Slaven Bilic at international level and could be moved on for the third summer running, amid the imminent arrival of Gonzalo Higuain from Napoli.
The same report, cited by Football Italia, claims another front man, Simone Zaza, has spurned the Irons' advances as he prefers to remain in Serie A.
However, the report adds the Hammers' hopes could be dashed if Inter Milan renew their interest.
And finally, a new name has emerged on West Ham's list of striker targets, according to reports in Spain, via Sport Witness.
However, the east Londoners could reportedly face competition from Barcelona in their bid to land 17-goal Deportivo La Coruna star Lucas Perez.