Fabregas has been at the centre of a summer-long conflict between the Gunners and La Liga champions Barca, who had a £30 million bid rejected for the star in June.
Barca president Sandro Rosell and the club's players have conducted a very public attempt to try to persuade Wenger that he should allow Fabregas to return to the club where he began his career.
Fabregas himself appeared to fan the flames earlier this week when he told a crowd of 2,500 Barcelona fans in his hometown that he hoped to "see them more often".
However, World Cup winner Fabregas returned to training with Arsenal on Thursday and former Gunners captain Sansom is certain the 23-year-old will at Emirates Stadium.
"I've had a chat with Arsene Wenger and he told me he's going to stay, which is great news," Sansom said. "It's a good day for the club, with all the fans being here to see Cesc back here, they all look up to him and it's great news that he's stopping."
Fabregas received a standing ovation from around 7,000 supporters at the Emirates. The midfielder seemed at ease with his team-mates throughout the 90-minute session, and waved to the crowd occasionally.
Former Arsenal goalkeeper Bob Wilson, who spent 11 years at the club, is also confident that Fabregas will stay after attending the training session.
"Today is the clearest indication you can get that he will stay," Wilson said. "If you look at the team photo for the 2010-2011 season, he is at the front of the picture.
"There will be an announcement soon that tells everyone that Cesc Fabregas is going to stay at the Emirates Stadium for this season, and for maybe longer."
Wilson feels Barca have behaved badly over the Fabregas affair and that their €35 million offer was never going to tempt Arsenal.
"I think everyone have been worried and everyone have seen that the way that Barcelona has handled things has been totally wrong," he said. "People have been comparing the possibility of Cesc going with Ronaldo going last year. Real Madrid paid £80 million for Ronaldo. They over-paid.
"Barcelona at this moment have offered a very paltry amount for a player who is one of the greatest players on earth."
He added: "I don't think we need to tell him that everyone at the club loves him. He has a second father at the club in Arsene Wenger and I think Arsene will be able to get his head around the fact that he is an Arsenal player and not a Barcelona player.
"Cesc owes a lot to this club in the same way that this club is very appreciative of everything that he gives to it."