De Gea is under contract at Old Trafford for another season, but has been linked with Real after failing to agree to a new deal with the Red Devils.
"If De Gea does come here, he will be welcomed," Casillas said to Spanish radio station Cadena Ser
"Competition is good and there is not a clause in my contract which states that I have to be number one
"In this club, you have to understand that any day they can sign a goalkeeper or any player and if that is going to increase the level, all the better.
"We have a good relationship and I will give him a helping hand.
"We will have to fight and compete for a place just like we do in the national team."
De Gea, 24, joined United from Atletico Madrid in a £17.8million transfer in 2011 and has made 133 appearances for the Barclays Premier League giants.
"De Gea is a great guy and is a goalkeeper for the present and the future," Casillas said
"He is a reality
He can handle pressure
"To have gone to a big club like Manchester United and shown his worth says a lot, and that experience has served him well."
Casillas is under contract with Los Blancos for another two years, and the Real and Spain captain has no intention of leaving any time soon.
"I don't see myself anywhere else next season," the 34-year-old said
"I've already said that I want to retire here
I would like to end my career at Real Madrid
"They (the club) recently told me they want me to continue.
"I am a man of challenges and last year I had a big one and I overcame it."
Casillas lost his starting place under former Real coach Jose Mourinho and also struggled at the World Cup, where Spain exited at the first hurdle.
Real signed goalkeeper Keylor Navas to a six-year deal last summer, and the Costa Rica international did make a handful of starts earlier in the 2014-15 campaign for the Spanish club, but Casillas regained his spot in the first XI.
"I've been at the centre of criticism this season," he said
"What hurts me most is those that say my career is over.
"Last season was a difficult one and I thought that this year would be the same.
"I've been here 25 years.
"If you always get an eight out of 10 from the fans, they then are not going to accept anything less.
"I share something in common with those that boo me at the stadium - we want for Real to win games and titles."
Real did not win any silverware in 2014-15.
They finished runners-up to Barcelona in the Primera Division and were knocked out of the Champions League in the semi-finals by Juventus.
Their disappointing end to the campaign led to the sacking of Carlo Ancelotti, who had guided Real to a record 10th European Cup in the 2013-14 campaign.
"The president and the board have taken the decision they think is best," Casillas said
"I could be angry as last season I didn't play that much, but the fact is that a great person (Ancelotti) has left and we wish him the best."
Source : PA
Source: PA