The France World Cup winner has been restricted to a bit-part role at Stamford Bridge this term, and Blues boss Frank Lampard would be willing to let him leave before the end of the transfer window.
Chelsea want to recruit a replacement before allowing Giroud to leave however, and a possible switch to Inter Milan now appears off the table.
But Giroud has now been linked with a surprise move to Spurs, with the 33-year-old understood to be open to that possibility.
Chelsea have been working hard to bring in a new striker this month, with Tammy Abraham sidelined with an ankle injury.
Lampard refused to dampen down links to Paris St Germain's Edinson Cavani after the Uruguay striker handed in an official transfer request.
Atletico Madrid have so far been unable to agree a deal with PSG for a permanent transfer for Cavani, while Chelsea have not been able to complete a loan move either.
Giroud spent six years at Arsenal before switching to Chelsea in 2018, and found the net as the Blues thrashed the Gunners 4-1 to lift the Europa League title in May 2019.
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