Scotland registered its first victory over its neighbours at Edinburgh on Sunday, bowling England out for 365 after posting its highest score of 371 for five.
“I can see us getting there in the next couple of years,” Tony Brian, chairman of Cricket Scotland, told the BBC.
“We’re so close to our goal of full member status now”. The International Cricket Council (ICC) has 12 full members, with Ireland and Afghanistan promoted in June last year.
The ICC has reduced the number of teams at the 2019 World Cup to 10 from 14, making it far more difficult for associate nations to qualify.
“The ICC set strict criteria for us to meet for full member status and we’re only two away,” Brian added. “We probably need one more win against a top nation and our women’s team, which is also rapidly improving, need to do well at a World Cup qualifier.”