Valverde’s position has come under increased scrutiny after the Nou Camp outfit lost 3-2 to Atletico Madrid in the Spanish Super Cup semi-final in Saudi Arabia last Thursday.
There have been reports that current Al-Sadd manager and former Barcelona midfielder Xavi has been approached to take over from the former Athletic Bilbao boss at the Nou Camp.
Iniesta played under Valverde in his final season at the club before departing for Japan outfit Vissel Kobe.
Valverde has led Barcelona to the La Liga title in each of his two full seasons in charge while they are locked level on points with eternal rivals Real Madrid in the current campaign.
Barcelona have however faltered in the semi-finals of the UEFA Champions League in each of Valverde’s two seasons despite boasting favorable first leg leads.
Nonetheless, Iniesta feels his former boss’ position is being undermined by the rumours circulating and has called for an end to them.
"What comes to my mind a little, if all this is so, is that the way everything is being done is a bit ugly," Iniesta told Onda Cero.
"I think that there should always be respect for the coach. The boss' situation and position has been left very weakened.
"My relationship with the boss is very good. During the year we have been talking sometimes. Really, beyond whether we like the coach or not, I think the situation is not pleasant for anyone: the coach, the team or the fans."
