The group, which opened its first site in Liverpool in 2010, and its second in Manchester in 2015, is aiming to open in Birmingham within the next 18 months.
It is also hoping for a second location in the suburbs of either Manchester or Liverpool.
The ideal sites will be between 80 to 150 seats.
Lunya is still self-funded, but in the future, husband-and-wife team Peter and Elaine Kinsella hope to seek outside investment for further expansion.
As well as its restaurant operation, Lunya also operates as a delicatessen, both in the physical stores and online, selling baked goods, food to go, and salads and dips, imported from Spain through specialist suppliers.
The group is aiming for 75% of all its Spanish products to be directly imported, and is also looking to open a warehouse to increase capacity.
“The Liverpool restaurant and deli, which already carries in excess of 1,300 items, is now seven years old,” says Peter Kinsella.
“Investment in a warehouse will enable us to negotiate better prices with producers and suppliers. Already, we have seen the benefit of that with reduced prices in our restaurant menu. We’re really excited at the prospect of a third site for Lunya with our research at an advanced stage.”