ECHO understands that the Canadian international striker is set to agree to personal terms after a second seven-figure offer was accepted by Liverpool on Friday.
Millar, 21, made 27 appearances for Charlton Athletic on loan in League One last season and sparked league interest, but Basel can offer Europa Conference football.
Liverpool rejected an opening offer for Millar earlier this week, but Basel have finally hit asking price and are close to confirming a deal.
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The forward made his Liverpool debut in February last year in the FA Cup replay victory over Shrewsbury Town, originally joining Fulham at the age of 17 in 2016.
Michael Edwards and Julian Ward had rejected previous standing offers for Millar – preferring to send him on loan to Kilmarnock and Charlton – when there was interest in the Bundesliga last summer.
Blackpool, led by former Liverpool Under-23 boss Neil Critchley, are also said to have been hoping to secure a deal this time around.
Millar still has 12 months on his current contract at Liverpool.