Solak offered his strongest backing yet for the German coach, and said he would consult players, supporters and club staff before making a final decision, but made clear that, if it were solely up to him, Eckert would stay at St Mary's.
"I think he deserves a second chance and I would give it to him. My full support would be behind him actually, because I think he's a super-talented manager," Solak said.
"I believe Tonda that he didn't know that it was the rule that he was breaking. My personal opinion, and the opinion of the board, is that he is a manager who deserves to be backed by us and to be supported by us. I will obviously seek advice from the team. I will seek advice from the players, from the fans. But yes, if it's ultimately my decision, he stays.
"I told him: 'You almost broke my heart. You do it again, you'll kill me. The next time I see you in July, if you don't know the EFL book of rules by heart, you can't work for me. Because, we can't have another mistake.' I truly hope that he will learn from this experience and he will achieve an incredible career."