Schalke confirmed that Chelsea made contact over signing Kolasinac, but that their approach was immediately rejected by the Bundesliga club.
However, Chelsea are free to negotiate a pre-contract for a free transfer in the summer with his contract expiring on June 30.
The failure to secure the 23-year-old is not expected to impact upon Branislav Ivanovic's possible move to Zenit St Petersburg and Schalke's president, Christian Heidel, spoke to Bild to confirm the offer.
"Yes, there was an approach [from Chelsea], but it was off the table immediately," and in a follow up interview with Germany's Sky Sports he said the rejected enquiry wasn't followed up by an official bid.
Schalke remain interested in renewing Kolasinac's contract, but are struggling in the Bundesliga and sit in 11th place. They are unwilling to sell their full-back after his understudy and Chelsea loanee, Baba Rahman, tore his cruciate ligament at the Africa Cup of Nations.
Juventus and Chelsea have both failed in attempts to convince Schalke in a cut price January sale, but could repeat their interest in the summer.