Il SecoloXIX, which is based in Genoa where Torreira plays his club football for Sampdoria, have today published a report saying the move is done.
The report states that Sampdoria were willing to sell only one of their star men – Dennis Praet or Torreira.
And it appears Torreira is that man with the deal expected to be completed after the World Cup.
Arsenal last week completed a move for Bernd Leno and Arsenal legend Nigel Winterburn thinks more signings are coming.
He told the Transfer Talk podcast: “There’s been a goalkeeper in, potentially the centre-half coming in, you’re talking about a centre-midfield player coming in.
“If you’d have asked me, those were the three positions I’d have listed to you straight away.
“In terms of attacking play we’ve got some fabulous attacking players. I’m just looking forward to having a structure now and the team will come together and use the pace we’ve got up front as well.
“It wouldn’t surprise me if we maybe looked at a wide left or right-sided player as well to come in. That’s a huge amount of players coming in in your pre-season budget when we are hearing Arsenal have only got £50million to spend.”
Winterburn says he expects Arsenal to be far more organised under Emery and believes more focus will be put on the defence.
“I said for a while with Arsene Wenger you know his style of play is open, it’s attacking, he likes both full-backs to be high and wide, and what that did is it gave Arsenal a problem when they tried to play out from the back and lost the ball in midfield areas,” he explained.
“That exposed the two centre-halves and their defensive frailties.
“I think with Stephan Lichtsteiner coming in, we were short of a right-back for someone to challenge Bellerin or injuries.
“Most people having been looking at the goalkeeper situation and saying Petr Cech has been a stalwart in terms of wherever he’s been he’s been fantastic in the Premier League but now might be the right time to bring in someone to again challenge him – if not take the No.1 position and see then what response Petr Cech has to that.
“I think it’s really intriguing but I think it’s also positive that the new manager has identified the positions that he thinks Arsenal need to be strengthened in.”