Issa, the chairman of the House Oversight Committee, represents a San Diego-area district heavy in high-tech businesses and has long been seen as friendly to the industry, the newspaper said.
"From a tech industry perspective, we have a very strong relationship with Congressman Issa. We've worked on a lot of issues with him over the years, including intellectual property issues," Peter Muller, director of government relations at Intel, told the Hill. "There's a good strong relationship and we think he'd be a good person to work with on immigration."
The industry is pushing for speedier approval of H-1B visas and green cards for workers with technical skills. Companies say the current process takes too long, and they have trouble filling open positions with U.S. residents.
Engineering groups charge high-tech companies are simply looking for cheaper labor.
Republican leaders hope a bill will be drafted before the Memorial Day break.