The Italian club thought they had clinched a deal to bring the 19-year-old attacker to Rome in the January transfer window, but a paperwork delay held up the agreement, and it ultimately failed to beat the deadline.
Anderson, who has been scouted by Chelsea and Tottenham on a number of occasions, will remain with Santos for the time being, but Lazio are hopeful of signing him when they get another opportunity this summer.
Lazio sporting director Igli Tare told La Lazio Siamo Noi: "The desire of the player and ours is to take this negotiation forward and conclude it in the summer.
"We did everything possible to sign him because he would have been the icing on the cake for us. We had an agreement and it should have ended positively.
"However, things then got complicated because his club and the fund who own 50 per cent of his contract couldn't agree on how to split the fee.
"We had agreed a £7m fee, plus 30 per cent of any future sale amount, but the two parties could not reach a solution."
The teenage forward plays alongside Neymar at Santos, having broken into the first-team following the departures of Ganso and Elano. He helped the club win the Copa Libertadores in 2011, coming to the attentions of Europe's top clubs during the South American equilavent of the Champions League.
The attacking midfielder has three caps for the Brazil under-20 team, and is under contract with Santos until 2016.