The 28-year-old Rennes player chartered a private jet on Wednesday afternoon to take him from Warsaw to Manchester Airport so he could get the deal done with Turf Moor chiefs, says the Lancashire Evening Telegraph.
Speaking to journalists in his homeland, Grosicki said: “There were complications.
“When I landed in Manchester it was still three hours to the transfer deadline, but many things were still not agreed.
“We were negotiating for almost two hours but we couldn't reach agreement.
“If I sign, what they offer me I wouldn't be happy at all.
“My dream was to play in Premier League and I was close, but I hope maybe I will get another opportunity to play in England.
“The deal was close. Burnley really wanted to have me and they were willing to pay big money.
“On the final straight, everything went wrong."