The Indian-based firm announced it was selling its loss-making UK business in March, putting thousands of jobs at risk, including 4,100 at Port Talbot.
There are two known bids, while the UK government could take a 25% stake in any rescue and may allow changes to Tata's pension scheme to help the sale.
But the steel market has picked up.
On Wednesday, Tata reported that losses narrowed in its fourth quarter.
It has led to speculation in the national media that the firm could perform a U-turn and not sell up.
"If that is the case, fine," Aberavon MP Mr Kinnock told BBC Radio Wales' Sunday Supplement programme.
"If they do want to stay we would welcome that in principle," he said.
"But I would also say in practice steelworkers in my constituency, their families and communities around them have been through hell in the last few years and certainly since March when the sale was announced.
"I think they'll be forgiven for treating any news that Tata is staying on board with a degree of scepticism and even anger.
"So I think we need a very clear set of guarantees from Tata that they will be in it for the long run, that there will be investment and they will be doing what's needed so we're not back at square one 12 months from now."
Tata would need to give guarantees it is in the UK steel industry for the long run if it scraps its planned sale of plants, Stephen Kinnock has said.