The 34-year-old goalkeeper is in talks with the club but it is reported that a one-year deal is on the table and he would prefer a longer-term agreement. McDowall would love to see Alexander stay as has established himself as a valuable member of the squad since arriving from Ipswich Town in 2008.
"We are in discussions with Neil. I don't know how far down the line it is but we have been discussing terms," McDowall said in the Daily Record.
"Would we like to see him stay? Absolutely. He has shown loyalty here and done well for the team. Neil is a good lad. He works very hard and is not a minute's trouble.
"Will it be sorted soon? Hopefully. It's up to those upstairs. We've told them we're happy with him so it's a matter of getting the numbers right."
Rangers are currently under a transfer embargo but can sign players who are available on pre-contract and register them in September, but McDowall does not expect much business to be done at Ibrox. Hearts defender Ryan McGowan was one player linked with a switch to Rangers but is now set to join Chinese side Shandong Luneng Taishan. McDowall said:
"It's no secret we tried to sign him before the transfer embargo came in. He's a player we were interested in at that time.
"I wouldn't expect us to be announcing too much. We have a league to win and it's important we focus on that. If other stuff happens then it will happen."