The North London pair have both been mooted as potential destinations for the England forward, with the 23-year-old reportedly unhappy about a lack of game time in his favoured position.
However, interim boss Ryan Giggs has quashed any rumours of a potential exit, stating that Welbeck is not for sale.
"We won't be selling him," Giggs is quoted as saying in the Express.
"We showed that the other night that bringing young players through is an important part of the club's culture and history.
"We wouldn't like to lose someone like Danny because he has done that, he has been here since eight or nine. So we want to keep him."
The news means that Arsenal and Spurs will have to look elsewhere when it comes to bolstering their attacking options.
Having watched their signature signing, Roberto Soldado, fail miserably in his first season in England, White Hart Lane officials will be hopeful of signing a more effective frontman this summer.
Arsenal will see Nicklas Bendtner leave the club at the end of the season, and with only Yaya Sanogo as back-up for Olivier Giroud, adding a proven striker to the squad will be a priority for Arsene Wenger.
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