Inter Milan expect to seal a deal for Eriksen this month, but Conte is unhappy with Mourinho's accusations in the press.
The Tottenham manager claimed that Conte should 'behave responsibly' when talking about other team's players.
"I think we should always be protective," Mourinho said last week.
"Nothing, nothing. When I see people with responsibilities, speaking about Eriksen...
"I think we shouldn’t speak about players from other clubs until they become our players I think we shouldn’t speak about players from other clubs."
Conte has responded by refusing to comment on the transfer market any longer for fear of being intentionally misinterpreted.
"I no longer talk about the transfer market," Conte said (via the Mirror).
"The last time I did it, someone we all know twisted my words so I won’t say anything anymore.
"I never said anything unusual about the January transfer market making it difficult for all coaches. Every time I say something, it always gets amplified or twisted."
The pair's spat is reminiscent of their time opposite one another in the Premier League when Conte was Chelsea manager and Jose Mourinho at Manchester United.
Inter are trying to get a cut-price deal done for Eriksen, but are currently below Tottenham's £20m valuation.
Conte made clear that the decision now rests with the club, not himself.
"The club has to decide if it wants to do something," Conte added.
"If it wants to do it at a good price for the market or take a different approach. I am just a coach, I leave that to them."
Eriksen has made 19 appearances for Spurs in the Premier League this season, scoring twice and assisting a further two times.
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