Chelsea Pitch Owners confirmed on Friday that they met Hammersmith and Fulham Council this week to discuss the future of Stamford Bridge.
CPO, who own the land beneath Chelsea's home of 107 years, held talks with councillors and planning officers over the viability of expanding the club's stadium.
The issue of where the Blues play their football in the coming years has proven highly controversial, with the club failing in October to buy back the Stamford Bridge freehold from fan-led group CPO, who they sold it to in the 1990s.
Their attempt was seen as a precursor to a move to a new 55,000-seater ground.
Chelsea would prefer to stay put but insist it is economically unviable to do so, something the council has contested as they seek to force them to stay in the borough.
CPO chairman Steve Frankham said in a statement: "Directors of Chelsea Pitch Owners this week (Monday 23 April) attended a meeting with councillors of the London Borough of Hammersmith & Fulham (LBHF) and planning officers. The LBHF reiterated their position - laid out in a statement from them on 9 March - that they would like Chelsea FC to stay at Stamford Bridge.
"They also explained they would be happy to assist the club further in exploring ways to expand the stadium's capacity, and that it remains their belief this can be done, although not without difficulty.
"The club has put an immense amount of time and money into exploring how to expand Stamford Bridge and believes there are serious planning difficulties and, in any event, it is not financially viable. It is the CPO board's intention to continue dialogue with both parties in the hope of producing more clarity on these crucial issues.''