Some options, based on credit worthiness.
https://www.cardrates.com/advice/credit-card-credit-limits/
https://www.cardrates.com/advice/credit-cards-with-10000-limits/amp/
https://www.cardrates.com/advice/credit-card-credit-limits/
https://www.cardrates.com/advice/credit-cards-with-10000-limits/amp/
@VanderSnoot wrote:My understanding is that any of the Visa Infinites (such as CSR) will have a $10k minimum (but also require a $10k limit on another card). I've heard United Club Card starts at $15k. I don't recall what cards in the same category as Amex Centurion offer, as those are a bit outside my range.
Except when they don't 
US Bank issues their US Bank Altitude Reserve Visa Infinite Cards at lower CLs such as $3,000. Might have even read about a lower limit.
Unlike the old days where Visa and Master Card used to dictate minimum credit lines it is 'free willy' today. Citi Bank issues revolving limits NPSL's down to $1,000 on some of their cards (unreal) that are World and World Elite Master Cards. Status just isn't what it used to be 
As long as I am on the roll, the revolving NPSL of $5,000 as set by Visa and Master Card was eliminated effective to August 1, 2015. What does this mean? It is totally up to the individual lender to do what ever their hearts desire on flexible spend card limits and they do! Will add, some of the lenders reported Flexible Spending to the credit bureaus and when they discontinued the requirement eliminated it from their cards but forgot to remove the reporting from the Credit Bureaus such as USAA Federal Savings Bank (no extra charge for that piece of important trivia).
Credit report seems good, but those are some low limits on current cards and other lenders will kind of use that to size you up. Not saying it will be really important, but a large CL on a current card would make them feel better about giving you a big one since it shows you won't go nuts with it.
They'll also care about your total revolving credit limits, more conservative banks won't want to see too much available credit relative to income.
From what I can tell your annual income is most important to getting a large initial credit limit.
CSR will likely be $10k or over if you are approved, that is a card for high spenders and they give CL accordingly. They started me at $20k on that thing and is was my highest by far. Altitude Reserve started me at $17.5k, it was after I had closed CSR a few months before.
No derogatory marks is huge, keep that up and you can eventually get whatever you want within reason as long as you have a decent annual income, but it can take time.
They'll also care about your total revolving credit limits, more conservative banks won't want to see too much available credit relative to income.
From what I can tell your annual income is most important to getting a large initial credit limit.
CSR will likely be $10k or over if you are approved, that is a card for high spenders and they give CL accordingly. They started me at $20k on that thing and is was my highest by far. Altitude Reserve started me at $17.5k, it was after I had closed CSR a few months before.
No derogatory marks is huge, keep that up and you can eventually get whatever you want within reason as long as you have a decent annual income, but it can take time.
I remember when i was looking for my first $10k card, I had cards at 6k and 7k - then i applied for a US Bank platinum - straight in at $18k, Once i had got this card, it seemed to trigger higher CLs across the board, it seems that once one lender shows confidence in you - others will follow 