The 45-year-old has been a co-host on breakfast show GMTV for 12 years but is said to be fed up with the early starts and wants to spend more time with his family in Belfast.
BBC One controller Lorraine Heggessey is said to be in advanced negotiations with the presenter to lure him to the corporation when his contract expires this summer, according to reports.
A GMTV spokeswoman said: "We are currently in negotiations to renew Eamonn's contract when it comes up for renewal in May."
Fiona Phillips is signed up to co-present GMTV until 2007.
"Her three year-contract was renewed last year," the spokeswoman added.
GMTV broadcasts every day between 6am and 9.25am. It is consistently the highest-rated UK breakfast time programme.
ITV now owns 75% of GMTV after acquiring SMG's 25% stake in October 2004. The Walt Disney Company owns the remaining 25%.
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