Debt collectors typically hold debts for about six months, so if you'll have more success making a payment arrangement in the first month or two after the collector contacts you. On the other hand, if you wait a few months before proposing a payment arrangement, the collector might refuse or push for a higher payment since it will be losing the account soon.
Note that if you make a payment arrangement with a debt collector, it can restart the statute of limitations on the debt. The statute of limitations limits the amount of time the debt collector can sue you for the debt. This time limit varies by state and is usually between three and six years, but can be as long as 15 years.
Before you suggest a payment arrangement, review your budget to figure out how much you can afford to repay each month. Don't let the collector push you into paying more than you can afford to. If the collector doesn't accept payment arrangements, you can put aside some money each month until you've saved up enough to pay the account in full.