French newspaper Le 10 Sport suggests that Valencia's prospective new owner, Peter Lim, will target Falcao as his first major signing this month once he completes the takeover.
Chelsea have been heavily linked with the Colombian international ever since his stunning hat-trick against the Blues in the 2012 Super Cup.
Mourinho has insisted that Chelsea are not in the market for a striker, and the Stamford Bridge boss looks set to tie up his first deal of the January window this week with Nemanja Matic set for a medical.
Valencia meanwhile remain cash-strapped, which means Lim's cash would be crucial to their January transfer hopes.
Having originally pledged €40m for transfers this month, the Singaporean has since upped the budget to €50m in an effort to demonstrate his interest. And Falcao is believed to be the player he wants the most.
As well as Chelsea and Valencia, French newspaper Le 10 Sport claims Real Madrid also remain interested in the former-Atletico star.