Burnley have confirmed the signing of George Boyd from Hull City for an undisclosed fee.
Blackburn have bolstered their defensive options by signing Everton's Shane Duffy for an undisclosed fee.
The French centre-back was a notable absentee from Sunday's pre-season training session in Germany, staying in the team's hotel despite no indication that he was injured.
Mathieu has been touted as one of Barcelona's top transfer targets this summer as they seek to strengthen their defence following the retirement of veteran captain Carles Puyol, but Valencia president Amadeo Salvo has publicly insisted that the club will only sell the 30-year-old if the Catalans pay his 20million euro (£16m) release clause.
The defender's absence from training inevitably generated suspicions that a move to the Nou Camp was imminent, but Nuno sought to cool the speculation in a press conference on Monday.
"He is a Valencia player, but we thought it was opportune that he rested so he would be in perfect conditions today," said the Portuguese coach, who took over the club earlier this month following the sacking of Juan Antonio Pizzi.
Nuno takes charge of his first Valencia game on Tuesday against Bavarian minnows SpVgg Bayreuth, who play in Germany's regionalised fourth tier.
Next up is a match with Bundesliga side Nurnberg, and then the club head to Peru and Chile for pre-season games with Allianza Lima and Universidad Catolica respectively, before taking part in the Emirates Cup at Arsenal's Emirates Stadium in August.
Midfielder Ever Banega has returned to Valencia following a loan spell with Newell's Old Boys in Argentina and travelled to Germany with the team, as has new signing Nicolas Otamendi and forward Carles Gil, recalled to the club after a year on loan with Elche.
Nuno admitted that there would be changes to the squad between now and the start of the summer but said no decisions had been made yet.
The club have sold left-back Juan Bernat to Bayern Munich and last week parted ways with Adil Rami, who has joined AC Milan permanently.
"The only player I can't count on is Rami, because he has left Valencia, but I can count on everyone else," added Nuno.