It was reported that three Bursaspor supporters were in hospital with knife injuries after trouble broke out at the match against Besiktas in Istanbul on Sunday night.
Around 1,200 Green Crocodiles fans travelled to the Turkish capital for the match, which ended 1-0 for the home side, and television footage showed police using batons and tear gas to break up clashes outside the Inonu stadium.
Almost 1000 Light Blues' fans will travel to Bursa for the final Group C game and, despite some frantic attempts by Bursaspor officials to prevent Saglam addressing the issue of their safety, he said: "There is no doubt that when Bursa hosts any teams, especially in the Champions League, it is with Turkish hospitality.
"Even when we hosted famous and important clubs before Glasgow Rangers, we had no security problems and even when we lost the games, there wasn't even a tiny problem.
"So for Glasgow Rangers, there will be no problem at all, the supporters and the press are welcome."
Bursaspor, in their first appearance in the Champions League, are still looking for their first point after five games.
Rangers, on five points and in third place, have already qualified for the Europa League while Manchester United and Valencia are through to the last-16 of the competition with only the top spot to be decided when they meet at Old Trafford.
Saglam is not surprised by the way the section has unfolded.
"We would like to be qualified for the last-16 but there is a logical explanation for our situation," he said.
"First, we are in the Champions League for the first time and if you compare the budgets of the teams like Manchester United and Valencia to ours, there is huge difference.
"You can't qualify by just buying a couple of good players.
"When the groups were drawn we expected Manchester United to be in first place and Valencia in second.
"We knew that we were to challenge with Rangers for the third position.
"We unfortunately could not beat Rangers in the away game and now the group is pretty clear, everyone knows our position but we want to finish with a win.
"If we qualify for next year, we could do much better."
Saglam will change his keeper for the visit of the Ibrox men with second-choice Yavuz Ozkan making his first appearance in the tournament.