The reports said the Swansea board did not plan to renew Carvalhal's contract.
"The club has tried to do things on the cheap, bring players in on the cheap".
'I think we did our best, me and my staff; we gave everything to the club.
Coleman would be available after parting company with Sunderland following their relegation from the Championship.
The former Sheffield Wednesday boss managed to lift Swansea off the bottom of the table and out of the drop zone, but recent results have seen them dragged back in.More news: PM Mahathir seeks pardon for old foe
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The new manager will be the club's sixth in two-and-a-half years, with Garry Monk, Francesco Guidolin and Bob Bradley also failing to establish themselves permanently. I saw him at Bournemouth and he looked void of ideas, the same against Southampton in the second half.
Southampton are pretty much safe but will be looking to keep it tight and not concede too many goals, especially if they hear Swansea have put a few past Stoke.
"They've got no creativity, no real goal threat, the recruitment has been poor", said Roberts.
The 52-year-old went on to enjoy an unexpected manager bounce, leading the Swans to five league wins from his opening nine matches, while he charmed both fans and pundits alike with his anecdotes and analogies. They were only able to sign one player in January, Andre Ayew from West Ham for £18million, and the striker has not scored for them.
He therefore replaced sacked Paul Clement who was shown the exit doors after poor performances this season in the Premier League. We still have the 100-point target to play for, though the players have eased off the pace a little in the last couple of games and I can understand that.