Messi trained alone indoors on Wednesday and Friday, but worked on the sidelines of a group session at Barca's home stadium, according to Spanish press.
La Liga leaders Barcelona play their first match since mid-March at Real Mallorca next Saturday.
Suarez will be fit to play for the first time since undergoing knee surgery in January after reporting feeling no pain following training.
Messi and Suarez have scored 38 goals between them in all competitions this season.
Barcelona lead Real Madrid by two points at the top of the table with 11 matches remaining.