Diego Simeone's side went three points clear at the summit of the table with their 4-0 victory over Real Sociedad, while Barcelona lost 3-2 at home to Valencia and Real Madrid drew 1-1 at Atletico Bilbao at the weekend.
Goals from David Villa, Diego, Joao Miranda and substitute Diego Ribas ensured Atletico rose to the top of the league for the first time since the 1995/96 season.
And Gibson believes the influence of Simeone, along with the quality within their squad, means they can claim their first title since 1996.
Asked on Revista if Atletico can win the title, he said: "Yes they can.
"They have been in the top two since the start of the season. It is the first time they have gone to the top. They are consistent.
"Every single player knows every little detail of what is expected of him. Simeone tries to remain with the same starting 11, particularly the back four and the goalkeeper. So that will be interesting to see how they last the pace.
"They have not conceded from a corner this season. They defend from the front, Diego Costa and Villa know exactly what is required when they are out of possession, and on top of that they have quality players.
"They can go the distance and they will go the distance."
However, Gibson's fellow Revista guest Henk ten Cate believes Atletico could falter in the final stages of the season due to a lack of strength in depth within their squad.
"It is fantastic and amazing," he said. "Nobody expected it. They are a team that play with a lot of fun and with a lot of discipline. They know exactly where there strengths are. They are very well organised."
"But if I look at the three squads I think their squad, their bench, is not so strong. Not as strong as Barcelona or Real Madrid.
"I am sure they will get to the quarter finals [of the Champions League] because they play AC Milan, and they are way better than Milan.
"So they will play a lot of games and the players will get tired and the pressure will build up. I have to see how they cope with that.
"I think Real Madrid will win the title. They have the quality and now they have the organisation, especially defensively. You can see that the team is improving defensively.
"They give away very few chances and they will always be able to score a goal with the players and the quality they have up front."