Alex has told ESPN FC he is set to sign a new contract with Paris Saint-Germain, despite being linked with a move to AC Milan.
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Alex's current terms at PSG are to expire in the summer, and reports in Italy had suggested he could be set to join Milan at the end of the season.
However, speaking after PSG's 3-1 win against his former club Chelsea on Wednesday, the defender outlined his intention to stay with the Ligue 1 champions.
"Yes, I think that this week or next I will have some news. Some good news," the Brazilian told ESPN FC.
"We will perhaps have to wait a little bit longer, but I think everything has been OK'd by the club and that I will be signing to stay here for one more year."
Alex, 31, will return to Stamford Bridge for the first time as a member of the opposing team when he and his PSG teammates travel to London for the second leg of that quarterfinal tie next Tuesday.
The centre-back also expressed his hope earlier in the season that a strong run of form up until the end of the campaign would see him called up to Luiz Felipe Scolari's Brazil squad for this summer's World Cup on home soil.