Rubuta ci gaba don wannan sakin layi - Reyes ya kasance memba na dogon lokaci na manyan 'yan wasan kwallon kwando na kasar Spain. Tare da manyan 'yan wasan kasar Spain, ya lashe lambobin yabo masu zuwa: lambar tagulla a EuroBasket na 2001, lambar azurfa a EuroBasket na 2003, lambar zinare a gasar cin kofin duniya ta FIBA ta 2006, lambar azurfa a EuroBasket na 2007, lambar azurfa a wasannin Olympics na bazara na 2008
, lambar zinare a EuroBasket na 2009, lambar zinare a EuroBasket na 2011, lambar azurfa a Wasannin Olympics na 2012, lambar zinare a EuroBasket na 2015, da lambar tagulla a Wasannin Olympics na 2016. Tare da Spain, ya kuma taka leda a gasar cin kofin duniya ta FIBA ta 2002, wasannin Olympics na bazara na 2004, EuroBasket na 2005, gasar cin kofin duniya ta FIBA ta 2010, da kuma gasar cin kofin duniya ta FIBA ta 2014.