The phrase "room for negotiation" means there is space or opportunity to make a deal, compromise, or come to an agreement between two parties. Full definition
So make the first offer... but leave room for negotiation because the other side will reject it. (lawyerist.com)
Once the order is placed, there is little room for negotiation on the part of both the student and the provider. (professaywriters.com)
If it was tough to get an offer accepted on a house from steep competition, you may not have much room for negotiation with your seller. (onqfinancial.com)