The club make their first appearance in the competition's final when they face Barcelona at Gothenburg's Gamla Ullevi stadium on Sunday.
Asked how she felt about Chelsea's chances of emerging with the trophy, Aluko told the PA news agency: "Very confident. I know Emma Hayes has the winning mentality that makes sure the occasion is one thing but getting a job done on the day is another.
"One of the reasons I'm confident as well is because I think Chelsea are not precious about tactical philosophies. If they can't go through you, they'll go around you, if they can't go around you, they'll go over you.
"Going into the game, I think Chelsea are far less predictable for Barcelona than Barcelona are for Chelsea, and for that reason, I think Chelsea will be able to deal with whatever threat Barcelona have."
Hayes' side have already retained the Women's Super League title and League Cup this season, and four days after the Barcelona match host Everton in the fifth round of the FA Cup, the final of which is scheduled for December.
Regarding Chelsea securing a quadruple, Aluko said: "They absolutely can. I think at this stage if we are talking about quadruple, it's very possible - but obviously it's not possible without the Champions League and they have to deal with that first."
Aluko had two spells as a Chelsea player. The second ran from 2012 - the year Hayes took charge at the club - to 2018.
"Their pursuit of winning is relentless and has been for a long time," said Aluko, who won 102 England caps and is currently sporting director at Aston Villa Women.
"I left in 2018 having played in a semi-final of the Champions League, having won FA Cups and leagues. Even that dressing room was incredibly committed to winning every single game.
"Fast forward three years, that hasn't changed. The winning mentality has just been fostered throughout the years.
"They are relentless and even in adversity in games they know how to get it done.
"They are a really different animal I think to deal with and for me the best team in the world right now, with the best players in the world."
Of Hayes - whose side are the first English team to reach the final of the competition since Arsenal, with her as assistant boss, won it in 2007 - Aluko said: "I think she's so effective because she's a visionary. I'm not lying when I say Emma Hayes predicted this nine years ago.
"When I signed for Chelsea in 2012 we had a really bad season, we were really bad, and I remember Emma Hayes distinctly saying to me 'we will bring in better players, better internationals, and we will win trophies'.
"Throughout that journey she's always looked at the Champions League as a big aim. So she's a visionary that executes her vision.
"She's been able to set a vision, recruit the players needed to execute that vision, she's also been able to manage the relationship with the club to support that vision, which is very important in women's football.
"And now she's there, and now really they've just got to cross that finish line."
:: BT Sport has live coverage of the UEFA Women's Champions League final between Chelsea Women and Barcelona Women live from 7.15pm on Sunday, May 16 on BT Sport 2.