The 26-year-old, who has missed the club’s opening four rounds with knee tendonitis, has been training with the team for over a week and trained strongly on Monday morning.
Club physiotherapist Matt Cameron said should the key forward get through training this week, he would likely play his first match for the 2014 season this weekend.
“He’s been training with the team now for a week or two,” Cameron said in this week’s HCF Injury Update.
“We’re expecting him to train fully this week and if all goes well he should be available this weekend.”
Speaking to the media on Tuesday afternoon, coach John Longmire said a decision would also need to be made on which level of football Tippett would play should he be available.
"He trained again yesterday and trained really well and pulled up well, so we expect him to play this week," Swans coach John Longmire told reporters at the SCG.
"The discussion will be whether it's reserves or seniors.”
Cameron also confirmed that dual Brownlow medallist Adam Goodes, who joined team training for the first time since January last Friday, was not far behind.
“Adam is only a session or two behind Kurt, so he’s going well,” he said.
“He trained this week and there will probably be another week of training for him.”
In other injury news, Sam Reid continues to make a slow recovering from an Achilles injury, which has sidelined him for the last two matches.
“His Achilles has settled and he’s been able to start running this week,” Cameron said.
“We’ll progress his running this week into next week and will make a decision about when he’s ready to train.
“It’s looking like it’s probably going to be a couple more weeks.”
Cameron also confirmed that Tommy Walsh, who resumed training a week ago after a long layoff from a serious hamstring injury, would be assessed on a week-to-week basis before a decision is made on his return date.
“Tommy has had a longer layoff, so we want to give him a good few weeks of training,” he said.
“We’re just seeing how he pulls up after each session.
“He’s doing bigger and bigger training time and we’ll make a decision next week or the week after about when he’s ready to go.”
