"I think that's in the realm of possibility. The president didn't commit, but I think he's very open-minded," the senator told reporters outside the White House on Sunday.
He added he knew some Democrats who would give money for the wall and border security if Trump guarantees that "Dreamer" immigrants, who came to the country as children, and people from areas ravaged by wars or natural disasters could stay.
"Hopefully, we can get some serious discussion started maybe as soon as next week," Graham said.
READ MORE: Trump Signs Order to Freeze Pay for Federal Workers Amid Gov Shutdown
Federal government agencies have been partially closed since December 22 after Democratic lawmakers refused to meet Trump’s demand for money to build the disputed wall on the US-Mexico border. The president rejected a Democratic deal that included $1.3 billion in border funding.