Damiao had been heavily linked with a move to Tottenham in recent transfer windows but reports have suggested that a switch to Ligue 1 could be on the cards.
The 23-year old is likely to be in high demand again this summer and Anigo admits he is someone Marseille have been keeping an eye on.
"Leandro Damiao? We know him very well, but there are financial aspects we cannot ignore. We are following him but it is too expensive so far," he told L'Equipe.
"The team needs to be attractive, getting reinforcements notably in attack with more speed on the flanks and ability to dribble.
"On a financial level we will be more at ease than last season, but we didn't win the lottery. Our priority is to try to sign French players. We need some youthfulness in the group, players with big desire to win titles.
"We would like to find explosive players on the wings, one defensive midfielder, an additional left full-back and another centre defender. If André-Pierre Gignac will remain we should not sign any centre forward.
"We are eager to keep all of our key players."