The best replacement for linen is cotton.

The best alternatives to linen are rated as following:
★★★★★  cotton
★★  cotton canvas
★★  canvas
★★  wool
★★  silk
★  wool suit
★  cotton suit
★  hemp
  twill
  chambray
  evenweave
  irish linen
  silk sakura bloom
  flax
  disposable
  pure white linen
  ramie
  muslin
  aida
  rayon

Your alternative for linen is not listed? Suggest!
Speaking about linen, one probably shouldn't forget about cotton.

Other search terms related to linen and their ratings are:
★★★★★ cotton
★★ seersucker
★ wool
You have in mind a companion for linen and it is not yet here? Propose!



Google Trends

Scale is based on the average worldwide traffic of linen in all years. Click on graph for more.
linen
cotton
cotton canvas