The Scottish international, who scored 11 league goals for the club last season, missed the final few months of the campaign with an Achilles injury.
He told the club's official website: "I'm doing well, it's a slow process as we are making sure the foundations are right as you have to make sure the ankle is strong before I put full weight on it.
"My ankle gets stiff in the morning and the evening, but that is normal because there has been a big trauma. Once I get going on it then it's all right. I am walking normally now.
"I'm happy with how it's going and I hope to get some minutes on the pitch in August, but the main aim is to be fully fit by the end of September. Anything earlier is a bonus."
The 29-year-old joined Brighton from Peterborough United in 2011.