Trundle, who has netted 20 times in 25 starts for Third Division Swansea this season, is eligible for the Republic of Ireland but Sanchez hopes to convince him and Swans team-mate Andy Robinson that his side will provide him with a better international career.
Sanchez said: "The Republic of Ireland manager Brian Kerr has been very dismissive of Lee's chances at international level - maybe because he plays his football in Division Three.
"But I'm very interested in Lee. I see him as a natural goalscorer and I'm going to look closely if he qualfies for us. There's a lot of politics in Ireland - it could be that either of Trundle's grandparents were born over the northern borders.
"I see Lee as just what Northern Ireland need right now, I'm not exactly blessed with striking options in my squad.
"His scoring record has impressed me over the last two seasons, he is a player I've been aware of for some time."