The United States international attracted interest from Germany but has stayed at Seattle since leaving college in 2014.
But it seems Morris is finally ready to try his hand in Europe after winning two MLS Cups with his hometown club.
The Athletic reports the 26-year-old has been given permission to leave the USMNT's training camp.
It is believed Morris will sign a loan deal with promotion hopefuls Swansea.
The Welsh club are currently second on the Championship table.