Hampshire chairman Rod Bransgrove says it could be "embarrassing" for cricket not to stage big international matches at The Ageas Bowl.
Bransgrove confirmed that he will be bidding for all the big international games when the next round of staging packages are up for grabs.
That includes the 2019 Ashes fixtures.
"We want to bid for the very best fixtures and that includes the Ashes series in 2019," Bransgrove told BBC Radio Solent's Hampshire cricket forum.
Hampshire's Ageas Bowl is yet to stage an Ashes Test despite bidding for the 2015 series, but with a major redevelopment of the ground expected to be completed in 2014, Bransgrove believes they have a "compelling argument".
The current list of fixtures run up until 2016.
The £38.5m revamp will include the construction of a four-star hotel, conferencing and hospitality facilities as well as a new media centre.
Work is due to be completed in time for England's next Test Match at The Ageas Bowl against India in 2014.
"Once this ground is complete it is going to be compelling argument and it might be a little embarrassing to ignore it," Bransgrove added.