Sealing the border has been described as "totally impracticable" by a local Senator.
The lack of an all-island strategy to deal with Covid-19 has led to calls for checkpoints on the border to prevent the spread of the virus.
The 2001 foot and mouth crisis has been cited as a precedent for the border to be closed when Gardaí and the Defence Forces were placed at crossing points.
However, local Senator Robbie Gallagher has said sealing a 300 mile border with almost 300 crossing points isn't feasible.
The Government has been criticised for not giving Gardaí the power to turn back people travelling from Northern Ireland without a valid reason.
Senator Gallagher says while the border can't be sealed, these powers are needed for Gardaí and the PSNI: