The highly-rated centre-back revealed last week that Rangers were keen on him and he has now been informed by his agent that Everton have joined the chase.
The Toffees sent scouts to Czech Republic over the winter to see Suchy in action and it now appears they could try to secure a deal.
"Yes, it is true that these two clubs are interested in me. My agent Pavel Vandas told me," Suchy told idnes.cz.
The 20-year-old claims that talks have already begun but he has yet to make a decision on whether he would prefer to move to Goodison Park or Ibrox.
"I cannot say. A lot depends on the first feeling from negotiations or on how much the coaches will want me in their team," he commented.
"At the moment there have been some opening negotiations going on."