Everton manager Roberto Martinez says he plans to make three new signings before the transfer window closes.
River Plate defender Ramiro Funes Mori, 24, watched the 2-0 defeat against Manchester City at Goodison Park.
Everton have also had talks with Dynamo Kiev for forward Andriy Yarmolenko yet reports suggest they may now move for Shakhtar Donetsk's Bernard.
"The fact that Ramiro Funes Mori was here was down to the agreement we have with River Plate," said Martinez.
Everton are also interested in Uruguayan striker Leandro Rodriguez, a 22-year-old who plays for River Plate Montevideo.
He has an Italian passport and has scored 19 goals in 71 games for the club.
Martinez also has a long-standing interest in taking Manchester United's Adnan Januzaj on loan.
That hinges on whether Old Trafford boss Louis van Gaal feels he needs to send the 20-year-old Belgian out on loan to get further game time.
Mori was on Merseyside with Everton now waiting on the results of a work permit application and a medical before completing a £5m move.
Martinez has also been in discussions for playmaker Yarmolenko - although reports in Ukraine indicated he has turned his attention to Brazil international Bernard as an alternative.
"This is a player who has won the Copa Libertadores with River Plate," Martinez said of Mori.
"He is 24 and a left-footed centre half with a winning mentality who will fit the squad extremely well.
"You don't get many opportunities to bring in a player who has won the Copa Libertadores."
"We are well advanced with that deal otherwise we wouldn't have permission to have him at the game."
Everton officials held discussions with their Dynamo Kiev counterparts in Monaco on Monday in an attempt to agree a deal for 25-year-old Yarmolenko, who is valued at around £15m.
Talks have continued but have proved tough to conclude.
Bernard, a 22-year-old who figured for Brazil in last summer's World Cup, has now been touted as an alternative to Yarmolenko although it was claimed in Kiev on Sunday that Dynamo are still considering Everton's offer for their talisman.
Martinez repeated his stance that his club have no intention of selling 21-year-old England defender Stones having rejected a third Chelsea offer of £30m and with Jose Mourinho now believed to be planning a fourth bid.
Asked again if he would keep Stones, Martinez said: "That's the plan. We have enjoyed his development and the way he has grown in the last two seasons.
"He just puts a smile on your face when you see John Stones defending.
"He is an incredible footballer and to be able to organise the way he does and control things at such a young age shows the type of footballer he is. I thought he was outstanding."