There are basically two strategies if you want to re-sign him.
The first is to make an aggressive offer ASAP. For this to work, your offer needs to be close to what he is demanding so that he is worried about losing money if he looks for better contracts and doesn't find one from another team before the offer comes off the table.
The second is to let the market decide. He is restricted, so the Celtics can match an offer sheet.
In the first case, you may end up bidding against yourself and pay more than you had to. In the second case, someone else may be willing to overpay and you might find yourself either paying too much or letting Sullinger go for nothing. I wouldn't be shocked if he gets paid more than Tristan Thompson next summer.
