Oviedo, who joined the Toffees from Copenhagen over the summer, has revealed he enjoys a close friendship with his international captain.
However, the 22-year-old is set to put that to one side ahead of Saturday's Premier League clash at Craven Cottage.
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"I spoke to him before I joined Everton and we still speak on the telephone. I congratulated him on the goal [he scored against Reading last weekend]. He is a very good guy and our national team captain. He is a good person.
"I spoke with him two days ago, he told me Fulham need the three points but I told him it is the same for Everton. Maybe after the game we will swap shirts."
Ruiz opened his account for the season in spectacular style against Reading last weekend, and knows what it takes to score against Everton having bagged a goal in this same fixture last year.
However, Oviedo insisted Martin Jol's side boast a number of other players who are capable of hitting the back of the net, and believes the Merseyside outfit will need to be at their best.
"I think Fulham has good attacking players; Berbatov, Bryan and Rodallega are good players so we will need to be careful," he continued.
"But we have a very good team, very strong defenders and good players in midfield and attack.
"It is very important for us to win this weekend because we what to stay in the top places. We need to win to keep close to the Champions League positions."
Although the versatile left-sided player is yet to start in the league for David Moyes's side, he did come off the bench for the closing stages of last week's clash with Liverpool, and enjoyed every minute of it.
"It was a very nice experience," he admitted. "I was looking forward to it and the atmosphere was amazing.
"I have played in derbies before but this one was very, very special. When I came to Everton everyone talked about the game and I am so happy to have played 10 minutes of it.
"The team has a strong mentality. We have come back from being 1-0 and 2-0 down in recent games and the team is very united."