The 32-year-old's current deal with Carlo Ancelotti's side is due to expire at the end of June, and there has recently been speculation surrounding his future in the Spanish capital.
Vazquez is not first choice at Bernabeu, but he has proven himself to a valuable squad member once again this term, contributing two goals and six assists in 32 appearances in all competitions.
The Spaniard starred against Barcelona in El Clasico last weekend, scoring once and providing two assists in an excellent performance from right-back, with Real Madrid winning 3-2 to move 11 points clear at the top of the La Liga table.
According to AS, Los Blancos are desperate to keep hold of Vazquez and are planning to extend his contract at the club for a further 12 months.
Lucas Vazquez 'in line for Real Madrid contract extension'Vazquez has scored twice and provided five assists in 25 La Liga appearances this season, while he has also come up with one assist in seven Champions League outings.
The Spaniard came through the youth system at Real Madrid and also represented Real Madrid C and Real Madrid B ahead of his first-team debut.
Vazquez joined Espanyol on loan for the 2014-15 campaign, making a permanent switch to the Catalan side at the end of the season, but Real Madrid then exercised a buyback clause to re-sign him.
The nine-time Spain international has made 343 appearances for his current side in all competitions, scoring 35 goals and registering 63 assists in the process.
Vazquez has spent the majority of his career as an attacker but has now developed into a right-back,
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