Rojo, 24, is an Argentina international and played in the World Cup final loss to Germany. He is currently under contract at Sporting Lisbon, although 50% of his rights is owned by player recruitment agency 'Doyen Sports'.
Sporting are believed to be pushing for their 25% of the fee to be worth around €5m, bringing the overall cost of the transfer to take Rojo to Southampton close to the €20m-mark.
The reason for Sporting only taking 25% of any potential fee lies not only with the presence of Doyen Sports, but also in that Rojo's former club, Estudiantes, are entitled to 25% of any future sale.
Gardos, 25, is a Romanian international and has represented his country on 12 occasions. He currently plays for Steaua Bucharest, although he has seen interest in his services from Dynamo Kiev, CSKA Moscow and Borussia Dortmund in recent times.
The chief executive of Steaua confirmed on Friday afternoon that Southampton were in talks to sign the defender, but admitted that the club would like to keep hold of the player until the outcome of their Champions League qualifier with Ludogorets is settled in late August.
Some reports in Romania suggested that Southampton have already completed a deal for the Romanian defender in a deal worth around £5m.
Southampton are understood to be keen to push the deal through as soon as possible following the loss of Dejan Lovren this summer - leaving them with only Jose Fonte, Maya Yoshida and Jos Hooiveld as their experienced central defensive options.
The Saints were reported to have lodged a series of bids for Rojo after executive director Les Reed jetted out to Portugal earlier this week. No bid has yet been reported as being accepted by the Lisbon club.
When asked firstly if Gardos was on his list for this summer's recruitment drive at St. Mary's, Koeman answered: "We are interested in the player but until now they haven’t told me that it’s signed or it’s OK. I don’t know, but we are interested, that is true."
Koeman was then pressed on whether the club held any interest in Rojo still, despite seeing two bids knocked back by the Portuguese side, and confirmed that the Saints still maintain an interest in the player.
When asked on how far the deal had progress, Koeman was slightly less committal.
"It’s more questions for the chairman and Les Reed," he said.
Southampton will hope to complete as many moves as possible ahead of the new Premier League campaign, which starts for them with a trip to Liverpool on Sunday, August 17.
However, chairman Ralph Krueger has called on supporters to judge the club's summer transfer business on September 1, stating that the club hope to develop a "better and deeper roster".
The Saints have added four new faces to date, with Fraser Forster expected to become their fifth acquisition over the weekend, with a medical scheduled for Saturday morning.
Will the Saints be able to land Rojo and/or Gardos?