Controcampo says Milan chiefs are prepared to send Gilardino away on-loan for six months in January to help him rebuild his shattered confidence.
Gilardino would welcome the prospect of working with Lazio coach Delio Rossi, which has opened the door to a potential swap involving Rocchi moving to the San Siro.
Rocchi, whose contract talks with Lazio have stalled, has offers from Bayern Munich and Monaco, but would prefer to remain in Italy.