Kilmarnock manager discusses future of Celtic target and Jack Hendry rumours
But the arrival of the Finland international sparked fears among the Killie faithful that owner Billy Bowie was gearing up to sell prized asset Taylor.
Celtic are rumoured to be readying a bid as they step up their search for Kieren Tierney's replacement while Nurnberg are believed to be interested in the 21-year-old.
However, Alessio says he is confident of keeping hold of Taylor following talks with Bowie.
He said: "I want two players for every position. We have Greg Taylor at left-back and now we have Hamalainen.
"We want to keep our best players and for this reason the situation with Celtic and Greg are just rumours.
"There are 10 or 11 days left of the market but we know our situation with Greg Taylor. It's only rumours.
"I don't know (what it will take for us to sell him) but I've spoken a lot of times about this situation with the board and Billy Bowie. We agree that we want to keep our best players. It's an easy situation.
"Greg is a good player in my team and I don't want to think about him going away.
"We're pleased to have Niko here. He's young and athletic and we believe he can make a good addition."
Hamalainen is Killie's fifth recruit of the summer but Alessio played down talk of a move for Celtic's Jack Hendry, although he is keen to add another centre-back.
The Italian said: "At the moment we're having a lot of conversations and we want to add new players this week or next.
"There are a lot of situations but at this moment only conversations.
"We need to complete the squad with another centre-back as we only have three."
Killie will look to put their first Ladbrokes Premiership win on the board when they host Aberdeen on Saturday.
They will have to put the shackles on eight-goal Dons hitman Sam Cosgrove, who has this week been linked with a surprise move to Italy.
And Alessio can understand why the frontman is on the Serie A giants' radar.
"We know him, he's a good player," said the man who helped Antonio Conte lead Juventus to three straight Italian league titles. "He's tall, strong, holds the ball up.
"At the moment, a lot of teams want the strikers like this, these are the typical skills they want.
"So I'm not surprised a big team like Lazio are looking at him."