Goal understands Monreal, whose existing deal is due to expire at the end of next season, has agreed a new contract with an announcement expected shortly.
The 29-year-old has started all but one of his side's Premier League games this term, helping Arsenal to the top of the table while also remaining in the Champions League and FA Cup.
Arsenal have previously been reluctant to offer long-term deals to players aged 30 or over and when Wenger was asked whether Monreal was in a rush to agree a deal before his next birthday in February, the Frenchman joked: "Certainly."
READ MORE | Wenger makes BOLD transfer prediction
But, turning to Monreal's impact since arriving at Arsenal from Malaga in 2013, he added: "[His importance has been the] regularity of his performances, the fact that he has improved every year since he arrived.
"He is not necessarily my first-choice left-back. At the moment he plays more than Kieran Gibbs but I think I'm a bit spoilt there because Gibbs has come back and has shown again on Saturday [that he plays] at a very, very strong level.
"That makes my decisions at that level very difficult but overall Nacho Monreal has been absolutely outstanding."