Sanchez has reportedly been offered a mega £400,000-a-week deal from an unnamed Chinese Super League club and is said to be using the offer as a way of persuading Arsenal into offering him a higher paid contract.
However, Nicholas has urged the forward to sign a new deal, as he is at "one of the finest clubs" in the world.
"Sanchez has won everything at Barcelona, he's won the Copa America with Chile, what else does he need? Do you need love, do you need care, do you need a birthday cake with candles on it?" he told 'Sky Sports'.
"I think the love of the game that he shows, the desire to still be a top player, tells me he wants to be in a top league with a top team. He's been at Barcelona, where else can he go? I think he's at one of the finest clubs he could ever wish to be.
"If he's happy, sign the deal. He'll get another wage top-up. I think when Cesc Fabregas was captain, he got another £5m a year or so from sponsorship so there are ways to do different pieces of business without always making it look like it's just a top-up in wages.
"Arsenal have got to make a point to say we don't need to spend £50m or £60m the way the other clubs are. Maybe once a season but let's focus on keeping these top players".