The north London rivals have both made enquiries for the midfielder but have been told Southampton will not accept any less than their valuation.
The Saints held firm last summer when they refused to entertain any bids for Schneiderlin as the player attempted to force a transfer to Tottenham.
The club are adamant that the 25-year-old will cost £25m this summer and will repeat the stance they took last year with Adam Lallana and Dejan Lovren.
Liverpool tried to negotiate over both players but eventually met Southampton’s demands for £25m for Lallana and £20m for Lovren.
Arsenal are prepared to spend up to £20m on Schneiderlin while Tottenham value the France international at around £15m.
Chelsea and Manchester United are also understood to be monitoring Schneiderlin’s situation with the player keen to move to a bigger club and play in the Champions League.
Southampton have offered Schneiderlin a new contract worth £60,000-a-week to stay at St Mary’s but he wants a fresh start after seven years at the club.
Schneiderlin’s relationship with the Saints board remains strained as he feels the club broke promises to listen to bids for him last summer.
The former Strasbourg man has missed the end of the season due to a knee injury after making 26 appearances for Southampton this season – and he may have played his last game for the club.
Southampton look set to qualify for a Europa League place next season but Schneiderlin has spoken of his desire to play in the Champions League.
“In August, I wanted to take a move but the club had lost too many players to agree to sell me,” he told French newspaper L’Equipe in March.
“Since then I have had discussions with the leaders and I want to play at the highest level: it is important at 25 years old to finally know the Champions League.
“Given that, late in the season, Southampton may qualify for the Champions League and I can stay, who knows. I have no desire to be in front of my TV on Tuesday and Wednesday.”