The UK bank is said to be in discussions with law firm CMS Cameron McKenna LLP to lease about 9,290 square meters of office space at the 125 London Wall building, Bloomberg reported.
The office would have space for about 1,000 workers is nearby the company’s headquarters on Gresham Street.
Lloyds plans to cut the number of its office locations in the capital by 30% to help make a one-off saving of £100mln. In London, Lloyds currently has six offices.
The lender expects the consolidation will deliver further annual savings of £100mln from the end of 2018. The restructuring will, however, cost about £300mln.
It is understood Lloyds is yet to sign a deal on the new space and other options could still be considered.
The new space became available after law firm Nabarro LLP moved into the offices of CMS Cameron McKenna following a merger.
Lloyds declined to comment on the report while CMS did not respond to requests for comment.
Under chief executive Antonio Horta-Osorio, Lloyds has also been cutting jobs with more than 45,000 eliminated since 2008.
In 2014 the group announced it would axe 9,000 jobs and last year said it would cull another 3,000 after Brexit.