The club said on Monday that they have written to the Board of Control for Cricket in India(BCCI) asking if the 32-year-old is available to replace Hodge, who will be on duty with Australia.
Laxman is in England with the India squad for the three-Test series which starts at Lords on Thursday, but won't be playing in the one-day series or September's Twenty20 World Cup.
He has 10 Test centuries to his name, including 281 against Australia in Kolkata in 2001, and has an average of 42.41.
"Our cricket manager Mike Watkinson is looking at all the options. Laxman is one of them," Lancashire chief executive Jim Cumbes told the Manchester Evening News.
"We wanted to check his availability and whether the BCCI can release him."