Pulisic has attracted plenty of interest this summer from Manchester United, Newcastle, Atletico Madrid and Juventus but is open to staying at Stamford Bridge on the condition that his playing time improves.
ESPN says open to letting Pulisic depart, the west London club initially favoured a permanent transfer and would have preferred not to hand the USA star over to a traditional rival such as Manchester United.
However, it is believed that Chelsea are now willing to listen to all offers and test the market should an internal agreement with Pulisic not be met.
The 23-year-old has featured in both Premier League matches under Tuchel so far this season, although each appearance was off the substitutes bench.
Pulisic is frustrated with the Blues manager for the manner in which he has handled his situation.