But they are expected to reject the invitation as they continue to oppose the LCB's Premier League proposals.
The LCB has turned to all 24 affiliated individual leagues in Lancashire - including the Ribblesdale League and Northern Leagues after a breakdown in talks between the LCB and the Confederation of Lancashire Cricket Leagues over the formation of a Premier League.
Lancashire League chairman Peter Westwell confirmed that there had been an invitation sent from Lord's but added: ``At the moment we are considering it but I don't think there would be any alteration to the way we feel. We don't think this is the way forward.''
The English Cricket Board is pushing for Premier Leagues to be established across the country to raise playing standards.
But the Lancashire League, keen to keep their clubs together in a more local competition, feel that development of players should come at a lower level.
The league currently has an under-18 side playing in a four-team tournament of two-day matches along with the Ribblesdale League, Northern League and Palace Shield League.
``It's a pilot scheme we would like to expand. The weather has murdered us but that has not put us off,'' added Westwell.
``We would like to carry it on in the winter with net sessions - and it could go up to under-21 and under-23 - to watch more players and then pass them up the pipeline.
``If Lancashire or other counties polish them at that level, they would have better players and we would have better ones coming back to us.'' Westwell admits that another league may take up the invitation to take on Premier status but added: ``So be it, but we will just get on with what we are doing.''
The LCB, following up the ECB's directive, are waiting to guage the response and are trying to see what the leagues would like in an attempt to find a solution to the problem.
But it's hard to see how this current approach will bring the formation of a genuine Premier league and a feeder league system any closer if the top leagues continue to resist.
And it remains to be seen what would happen if one of the lesser leagues accepted the invitation while those 'above' them did not.
Part of the ECB's plan is also the introduction of two-day matches with an innings on consecutive Saturdays and are seeking applications from premier leagues regarding pilot schemes during the 1999 and 2000 seasons.
But Westwell also believes that is a non-starter on logistical grounds.
``Common sense rebuffs that. I don't think that would work. That's not just me but the general feeling of leagues in Lancashire,'' he added.
``We all want a good England team and I watch the county when there are not league matches. I am not anti, but this is just totally the wrong set-up.''