Valverde is weighing up his future after Saturday's Copa del Rey final defeat to Valencia.
Allegri's initial plan is to take some time off, Goal reports. However, the doubts about Valverde's future could see him change his plans.
The Italian would jump at the chance to move to Barca this summer.
Other names such as Holland coach Ronald Koeman, the ex-Barça player, have been linked with the job should Valverde depart this summer.