The Denmark international has featured regularly for Fulham in the Premier League this season after joining on loan last summer.
But the Cottagers’ relegation makes a permanent move unlikely, paving the way for a transfer battle between the north London rivals.
Spurs like the player and he could be available for £20 million.
However, the squad will need to be trimmed before any move is made, as Ryan Mason currently has five centre-backs in his squad.
Arsenal view Andersen as a potential replacement for David Luiz, who is out of contract in June.
But the Gunners are unlikely to be able to offer new signings European football next season, which could make it harder to attract players.
The 24-year-old has made 29 Premier League appearances at Craven Cottage this season, scoring one goal, and has frequently captained the side.
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