The SPL champions are fully aware the wage demands of the Colombian striker – who rejected the offer of a new contract from Wigan – could take him well outside their reach.
But the 26-year-old is the kind of hitman Neil Lennon wants to add to his squad.
And, while signing a goalkeeper and a central defender are also on the shopping list – Fraser Forster and Leicester's Matt Mills remain the No.1 targets for these positions – the bulk of Lennon's transfer kitty is being earmarked for a striker to play alongside the club's top scorer for the past two seasons, Gary Hooper.
Lennon has confirmed they would be prepared to spend £4-5million on the right man, and Huddersfield's Jordan Rhodes could be available for that kind of outlay.
But alternatively that money could be invested in wages for a Bosman, if the right man can be identified, as was the case with Joe Ledley when he rejected the chance to sign for Premiership and Italian clubs to join Celtic.
Rodallega – who became Wigan's all-time Premier League scorer after joining from Necaxa for £4.5m in 2009, but who dropped out of boss Roberto Martinez's plans towards the end of last season – would prefer to remain in the English top flight where wages are higher.
But despite making it known three months ago he would be running down his Wigan contract which ends this month, he remains unattached.
Wigan's outspoken chairman, Dave Whelan, criticised the player's representatives for ill-advising Rodallega.
Whelan said: "Sometimes the lads must realise their agent wants the money more than they do."
The option to move to the SPL – even with the chance he could play in the Champions League, if Celtic get through their qualifiers – may simply not be enough to satisfy the demands of Rodallega.
But Celtic recognise that, unless they make their pitch, they will never know.
Forster's agent, Mark Curtis, has confirmed that talks over securing the keeper on a permanent contract will continue with chief executive Peter Lawwell this week.
And, despite interest being shown by QPR and West Ham, Parkhead remains the giant shot-stopper's preferred option.
Lennon's transfer kitty will be enhanced when he offloads some of the players he has listed as surplus to requirements.
And Efrain Juarez could be first to go, with Club America ready to offer him a way home to Mexico, if they can cut a deal with Celtic.
Daryl Murphy is another fringe player in demand, and Ipswich – where he spent last season on loan – hope they can land him for a cut-price £300,000.
Also on the way out is 21-year-old defender Josh Thompson who is on the radar of Carlisle.