The Czech Republic fullback has managed just eight Premier League appearances this season and has revealed a proposal from Fulham.
“I’m torn about all this because West Ham didn’t let me go to Fulham on deadline day (in January). I guess not many people know about this,” he said in an interview with Mladá fronta Dnes.
“In the dressing room after the match (against Chelsea), I look at my phone and there are four missed calls from my agent. Plus, a message: ‘Call me immediately’.
“Fulham offered great conditions. Karol (Kisel, Coufal's agent) asked: ‘Would you like it?’ I said: ‘Why not, if there’s no use at West Ham’.”
However, the Hammers blocked the move on deadline day.
“I’ll be 33 and it made sense to me, although I love West Ham and could imagine finishing my career there,” he said.
“As for Fulham, I would stay in the Premier League and even in London. We really like it there. My son has started playing in the West Ham academy and is doing better than I expected.
“My daughter will be going to school next year. How do I explain to them that we are moving to a completely different place? That is why I need to hear from West Ham so that I can consider what to do next.”
Off contract in June, Coufal says a move to Fulham could be revisited this summer.
He added, “When I am free, anything can happen."